1) broken calculator: 458+548+354 You would have to put in: 448+448+344 You will have leftovers from the original number.Then you would add them, You should get: 1,240 You would take your answer and add the leftovers that you had from before. The leftovers are: 10 from 458, 100 from 548, 10 from 354. When you add them up you should get: 1,360. To check if it's correct you would add:458+548+354 on your calculator and you would then get: 1,360. If this doesn't make any sense sorry if it is confusing.

1.) BROKEN CALCULATOR: Yes, there are more than one method to solve this problem. But what I think is the best is changing 50 or 500 to any numbers that can add up to that number. ( to make this easier, use friendly numbers like 30+20, 10+40,200+300 and 400+100 ) eg. 458+548+354 400+30+20+8= 458 458+200+300+40+8= 1,006 1006+300+20+30+4= 1,360.

2.) SHAKE HANDS: We could solve this problem by using PROBABILITIES.

BROKEN CALCULATOR If the key was broken, I would solve this problem by changing the question to 448+448+344, and add the sum of what I subtracted (to create the "new" question) to the answer of the question. (10+100+10=120=REMAINDERS) (ANSWER: 448+448+344=1,240+120=1,360) Yes, there is more than 1 way, but I "prefer" this way because I chose the number that is 1 less than 5, which makes it easier to add the remainders and the new question.

HANDSHAKE Question: How many times can 10 people shake hands with eachother? The same two people shake hands only once. Can you find the pattern?

I made a chart and charted down the sample space for how many combinations, and crossed out the combonations that already have been written on the chart.

Answer: 10 people can shake hands with eachother 45 times. Yes, the pattern is that the amount of combos gets lower by 1, whenever you go up by 1 person. EXAMPLE: Person #1= 9 combos Person #2= 8 combos Person #3= 7 combos

(When I was done charting down the combonations, it looked like block of stairs.)

Question 1: Broken Calculator Instead of adding 458+548+354. I would have added 408+448+344=1200. Then I would take the leftovers of the numbers then add the up (50+100+10=160). Then 1200+160= 1360

Question 2: Handshakes I did a probability tree to solve this question and I got 90 different handshakes in total because each person shakes hands with 9 other people. So 9x10=90

The method I found easier, for me, was to change the numbers from 458+548+354 to 448+448+344. When added altogether it should add up to 1240. The leftovers from each number:10,10,100 should add together and equal 120.Afterward, I added the two numbers together and got 1360.

HANDSHAKE:

Can be solved by using probability. I organized my outcomes.Which looked like this: 1- 2,3,4,5,6,7,8,9,10 2- 3,4,5,6,7,8,9,10 3- 4,5,6,7,8,9,10 4- 5,6,7,8,9,10 5- 6,7,8,9,10 6- 7,8,9,10 7- 8,9,10 8- 9,10 9- 10 10- So 10 people can shake hands with each other 45 times.

Yes, There will be more than one method to solve this problem. I solved this problem by changing the numbers. I took away 10 from 458 to equal 448. I took another 10 away from 354 to become 344. Then I took away 100 from 548 to give us 448. When you add our "new" numbers together it gives us a total of 1240. Now add the leftovers together, 10+10+100=120. Lastly add 1240+120 to equal 1360.

Problem 2- Handshake

I would solve this problem using probability. I would have to show you all my work. For this problem, I used a T-chart to organize all my numbers.

1.broken calculator: 458+548+354=? change 458 to 460 then change 548 to 648 then change 354 to 360 - to 108=1360 2.handshake: i will use probabilities to solve this question.

1)broken calculator. 458+548+354 i have a another method to add this without using 5. what I did was I changed the numbers and I got 408+48+304 so i added that and i got 760, but i still have 50,500,and 50 so what i did was I i i had to think of numbers to make that number so i went from 50 to 20+30 and 500 to 200+300, then I added 20+30+20+30+200+300 and I got 600 so after i added 600 and 760 and got 1360.

2)Hand shake What i used here is probability. 1-2,3,4,5,6,7,8,9,10 2-3,4,5,6,7,8,9,10 3-4,5,6,7,8,9,10 4-5,6,7,8,9,10 5-6,7,8,9,10 6-7,8,9,10 7-8,9,10 8-9,10 9-10 10- so the answer is 10 people can shake hands 45 times

Broken calculator: What I did was, break it down and kind of used expanded form. It would be easier if you use friendly numbers. eg. 400+40+10+8=458 300+200+40+8=548 300+30+20+4=354 So now I added them all up, the answer I got is 1,360.

Hand Shake: This can be solve using probability. I did my work in my notebook.

Broken Calculator: I found this easier, for me, was to change the numbers from 458+548+354 to 448+448+344. When added i added it altogether it gave me 1240. the numbers that were left over from each number are :10,10,100 altogeather it gives me 120.then , I added the two numbers together and got 1360. . 2)SHAKE HANDS. we can solve this problem by useing probibility.

Instead of having to add that, I found a method that was easy for me to do:

448+448+344

Now you have leftovers of the numbers, which are 10 from 458, 100 from 548 and 10 from 345. You then add them together:

10+10+100=120 448+448+344=1,240 120+1,240=1,360

2) Handshake

I solved the problem using probability. For me to organize the outcomes, I used a chart. And, the answer is that 10 people would shake hands with each other 45 times.

Yes there is more than 1 way. I took away ten on each number. So it would be.. 448+448+344. You would get 1,240. Then you would get 10, 100, and 10 again. You add the leftovers, then you get 1,360.

Broken Calculator: first i would change 458 to 408, 548 to 48, 354 to 304. then I'll add them up and get: 760. then I'll add 50+500+50, we cant use 5' so ill change it to: 50 to 20+30, 500 to 200+300, then 50 to 20+30. add them up: 200+300+30+30+20+20=600. 600+760=1360 the answer is: 1360

Handshake: this problem can be solved by using a probability chart.

Broken Calculator: Original:458+548+354 Mine:408+48+304 I left out the 5's and so I was left with 50,500,and 50.So I tried making them even.500= 2+3=5 200+300=500 then the 50 will just be added to the other 50 which makes it 500. Answer:408+48+304+200+300(500)+100(50+50)=1360 This is my answer.

1)Broken Calculator: If my calculator broke and I had the math problem 458+548+354 I would replace the 5's with 6 so that I could use my calculator to solve the problem.You will also have to subtract from the answer you get because your answer will be greater than the actual answer. You will have to subtract the amount you added to the question in the beginning which was 120. Example: 468+648+364=1480 1480-120=1360

2)Shake Hands: For question 2 I used probability. I organized my outcomes using a T-table. Example: 1- 2,3,4,5,6,7,8,9,10 2- 3,4,5,6,7,8,9,10 3- 4,5,6,7,8,9,10 4- 5,6,7,8,9,10 5- 6,7,8,9,10 6- 7,8,9,10 7- 8,9,10 8- 9,10 9- 10 10- 10 has already shaken hands with everyone.

10 people can shake hands with each other 45 times.

Instead of adding 458+548+354 I subtract 10 from 458, 100 from 548, and 10 from 354, which leads me to 448+448+344. It should be equvilent to 1 240. You then add 10+100+10 which we got from taking it away from 458+548+344. It should equal 120. After that add 120+1 240 and you get 1 360.

2. Handshake

To answer this, you would have to use a probability sample space, but you also have to ensure that to people do not shake hands more than twice(eg. 2,1 and 1,2) Each number represents one person.

(1,2) (2,3) (3,4) (4,5) (5,6) (6,7) (1,3) (2,4) (3,5) (4,6) (5,7) (6,8) (1,4) (2,5) (3,6) (4,7) (5,8) (6,9) (1,5) (2,6) (3,7) (4,8)(5,9)(6,10) (1,6) (2,7) (3,8) (4,9) (5,10) (1,7) (2,8) (3,9) (4,10) (1,8) (2,9) (3,10) (1,9) (2,10) (1,10) =39 possibilities all together. A pattern that I noticed is that the second digit will be one less than the one below it. Example, 1,2 <--- 1,3 <--- 2,3,4. 1,4 <---

1) Broken calculater 458+548+354= 1360 S.S. If the 5 key on your calculater is broken the awnser is 1,360

O.A. 0 50,000

M.I. 400+400+300+58+54+148= 1,360

Yes there is more than 1 way to solve it. I like the way i did it best cause its easy.

2) Hand shaking S.S. Ten people can shake hands forty four times.

O.A. 0 1000

M.I. #1 shakes hands with 9 people #2 shakes hands with 8 people #3 shakes hands with 7 people #4 shakes hands with 6 people #5 shakes hands with 5 people #6 shakes hands with 4 people #7 shakes hands with 3 people #8 shakes hands with 2 people #9 shakes hands with 1 person The pattern is it goes 9,8,7,6,5,4,3,2,1

1) BROKEN CALCULATOR: 458+548+354 I know that there are many methods to solve this, but I chose the easiest one, and that is to just replace or fill up the numbers that are missing with other numbers except for five. 400+38+20= 458 400+100+48=548 200+100+48+6= 354 458+548+354= 1,360 2) I just used probabilities to solve it.

I would solve this problem by just adding: 408 + 048 + 304 Which add up to: 760 I got this number by taking out the fives in the digit places so they become leftovers. Now 50, 500, and 50 is left. Change the 50's into 40 + 10 40 + 10 which equals to 100. Then add 400 + 100 + 100 Which equals to 600. then add 760 + 600 = 1360

Handshake Problem:

For this problem you could use probability but I chose to use pictures. For my answer I got 45 times 10 people can shake hands with each other.

1 broken calcaulator: 458+548+354 A) yes there is more than one way there is this way where you would have to put this in 448+448+344 so you would add that up and still remembering about the 10 10 100 left so i would ad those other numbers up so it would be 1240 then adding the 5 from your head it would be 1360.

B) i like having to use the 5 on the calculator because it would make things more easier.

2 handshake: i had wrote down my outcomes which looks like this: 1 2 3 4 5 6 7 8 9 10 1 3 3 5 5 7 7 9 1 4 3 6 58 7 10 1 5 3 7 59 1 6 3 8 5 10 1 7 3 9 1 8 3 10 1 9 1 10

1)BROKEN CALCULATOR: Since you cant use the five, you should just use the other numbers. Example: 1000+300+60,600+600+100+60 or 700+400+200+60. Then it will equal 1360.

2)SHAKING HANDS: For that question you would need probability.

Yes there are more than one method. I would change 458+548+354 to 448+448+344. There are leftovers from the numbers so it should add up to: 1240. The leftover from each number:10,10,100would add and equal 120 so then i add 2 numbers to equal 1,360.

BROKEN CALCULATOR I wouldn't do 458 + 548 + 354 I would do 400, 30 + 20 + 8 which will be 458, 300 + 200 + 40 + 8 which will be 548, 300 + 30 + 20 + 4 is 354

All of them together will equal to 1360

HANDSHAKE: I could solve this by using probabilities.

Broken Calculator: 458+548+354 For this problem I would replace the fives with fours then add the new numbers together. 448+448+344=1240 After that, add 10+100+10=120 1240+120=1360

Handshake: For this problem I made a probability chart. I wrote down all the possible outcomes and then I took out the numbers that were already used. The answer I got was 45. My chart looked like this: 12345678910 2345678910 345678910 45678910 5678910 678910 78910 8910 910 10

1) Broken Calculator: 458+584+354 I would do is put in: 408+84+304 Then i add them all up Got 796. But I still left with 50,500,50.So i did was make them even like 200+300=500. Then the the 50 i just add both of them to make a 100. Answer: 408+84+304+200+300(500)+50+50(100)=1.360 2)Handshake: I would solve it by using probability.

Broken Calculator: What I did was subtract where I saw the number five. I subtracted 40 from 458 which made 418, then I subtracted 400 from 548 which made 148, and then I subtracted 40 from 354 which made 314. Then I added 418+148+314=880. Then I added 40+40+400=480. I added 880+480= 1360. That is one of the ways I used to figure out this question. I am sure there are more than one way to answer this question.

Hand shaking: I used Probability. The first personn can shake hands with nine people, the second person eight, third seven, fourth sixth, fifth fifth, sixth fourth, seventh three, eighth two, nine one, and the tenth person already shook hands. So that would come down to ten people shaking hands forty five times.

Broken calculator: 458+548+354, I multiplied the numbers by 2 then added them all up. Then i followed by dividing it by 2. (458x2=916,548x2=1096,354x2=708 708+916+1096 = 2720/2 = 1360) Handshake: What I did was use probability to solve this. My answer ended up being 45, I got 45 because the first person can only shake hands with 9 people, the second can only shake with 8, third can only shake with 7, fourth can only shake with 6, fifth can shake with 5, sixth can shake with 4, seventh can shake with 3, eighth can shake with 2, ninth can shake with 1 and the tenth cant shake with anyone.

1) Broken Calculator: I did the same thing as Bennette. (making friendly numbers so it would be easier to add) Question: 458+548+354=? 400+40+10+8= 458. 200+300+40+8= 548. 300+20+30+4= 354. Then add all the numbers together. & I know it seems like a lot of work, but you're still getting the answer. :)

1) Broken calculator I did it this way: 408+48+304=760 Then I added 100 from the two 50s. 760+100=860 After, I added 200 and 300 to make the 500. 860+200+300=1360 My final answer is 1360. This to me was the easiest way.

2)Handshake To solve this problem I used probability. 1 - 2,3,4,5,6,7,8,9,10 = 9 shakes 2 - 3,4,5,6,7,8,9,10 = 8 shakes 3 - 4,5,6,7,8,9,10 = 7 shakes 4 - 5,6,7,8,9,10 = 6 shakes 5 - 6,7,8,9,10 = 5 shakes 6 - 7,8,9,10 = 4 shakes 7 - 8,9,10 = 3 shakes 8 - 9,10 = 2 shakes 9 - 10 = 1 shake Then add up all the shakes. It all adds up to 45 shakes.

1) If the 5 key is broken on my calculator I would use this: 367+630+363 To get the answer of 1,360 and yes there are more than one way. The best way to me is to to change the 5's to any number and try to get close to the right number by changing other digits.

2) For the hand shakes I made this: 1-2,3,4,5,6,7,8,9,10 2-3,4,5,6,7,8,9,10 3-4,5,6,7,8,9,10 4-5,6,7,8,9,10 5-6,7,8,9,10 6-7,8,9,10 7-8,9,10 8-9,10 9-10 The sum of all shakes is 45 shakes. The pattern is that the number is getting less every time you hand shake someone.

I would turn all the 5's into 4's so the question would look like... 448+448+344=1240 I know that I had to subtract to change the 5's to 4's so now I must add those back. 10+100+10=120 and then I would add that to the first answer 1240+120= 1360

Another way it could be done is by changing the 5's into 6's so the question would look like 468+648+364=1480. I added numbers to change the 5's to 6's so I would need to subtract them from the total. 10+100+10=120 1480-120=1360.

I like the first one better because it is easier to add than to subtract.

2. Shake Hands

There is a patter to figure it out. The first person will shake hands with another person 9 times and each person after that will shake hands 1 less time than the person before them. For a total of 45 handshakes between the 10 people.

Or you can use a chart

1 2 3 4 5 6 7 8 9 10 1 O $ $ $ $ $ $ $ $ $ 2 X O $ $ $ $ $ $ $ $ 3 X X O $ $ $ $ $ $ $ 4 X X X O $ $ $ $ $ $ 5 X X X X O $ $ $ $ $ 6 X X X X X O $ $ $ $ 7 X X X X X X O $ $ $ 8 X X X X X X X O $ $ 9 X X X X X X X X O $ 10X X X X X X X X X O

$ - hand shake X - have already shaken hands O - you can't shake hands with yourself

1. Broken Calculator 458+548+354 I answered this by breaking up each number with 5 into smaller numbers. For example, I took, 500 and broke it into numbers like 200+300. I answered it like this: 400+200+300+8+400+100+40+8+300+30+ 20+4=1360

2.Handshake I answered this by probability: 1. 1,2,3,4,5,6,7,8,9,10 2. 1,2,3,4,5,6,7,8,9 3. 1,2,3,4,5,6,7,8 etc.

well mine is like marilen's cause if you cant type 5 in the calculator you can just type like for example you want to type 500 you can type 300+200 instead in the calculator and ur not using the number "5".

1) Broken calculator: This way is only one way of doing it. First change every single 5 to a 4 so that you should have: 458+548+354 ----> 448+548+344 Now you add it, you should get 1240. Knowing you've changed every 5 to 4 now you just add 1, 10, or 100 depending on which place values you changed. In this case you should have 120 in total to add to 1240. You should get 1360.

2) Hand shake In this problem you can use probability to answer it. Knowing that there are 10 people shake hands with each other, show who each person shakes hands with, example: Person 1: 2,3,4,5,6,7,8,9,10 Person 2: 3,4,5,6,7,8,9,10 Person 3: 4,5,6,7,8,9,10 So if you get to the tenth person it would show that each person has shaken hands with one another. In total 10 people can shake 45 times.

1)broken calculator:458+548+354 you need to subtract: 458 by 10 548 by 100 448 by 10 the problem would then be 448+448+344+120=1360 2)shake hands: I used probability do do this problem.

A)BROKEN CALCULATOR: First, find every number's place value.Then, when every value of 5 is all revealed, change it addends that don't require 5(use happy numbers) and when is summed up, it is equal to the value of five. Lastly, add them all up in the normal way.

1)Broken Calculator What I did to solve this problem was rewriting the question to: 448+448+344=1240 Then I added the numbers that I took away. 10+100+10=120 Then I added 1240 and 120. The total I got was 1360.

2) Handshake To solve this problem, you could use probability. I wrote out my outcomes like this. 1- 2,3,4,5,6,7,8,9,10 2- 3,4,5,6,7,8,9,10 3- 4,5,6,7,8,9,10 4- 5,6,7,8,9,10 5- 6,7,8,9,10 6- 7,8,9,10 7- 8,9,10 8- 9,10 9- 10 10- So 10 people can shake hands 45 times.

For the calculator instad of typing in 458+548+354 I would type in 408+20+30+200+300+48+304+20+30 this way can be reapeted with ervery number up to 5. For the handshake every person would get a number from 1to10 and everyone shakes hands with ten then everyone exept 10 shakes hands with 9 and so on and that would be the pattern and the answer would be 45.

1)broken calculator: 458+548+354 You would have to put: 448+448+344=1,240 Now the remaining numbers would be 10 from 458, 100 from 548, 10 from 354. Add them up and u get 120. 120+1240=1,360.

1 - The Broken Calculator To solve this problem, I would add the first and last numbers first - I would add 10 to the first number and subtract 10 to the last number, eliminating the need for the five key. eg 468+344=812 To add the remaining number, I would add 100 to it first, then subtract 100 from the total, again eliminating the using of the five key. eg 812+648=1460-100=1360,the answer. There are other ways to do this problem, but this is my favourite. 2 - The Handshake If you think correctly, person #1 can shake hands with everyone but himself, resulting in nine handshakes. Person #2 can shake hands with everyone except himself AND #1, resulting in 8 handshakes. Person #3 can shake hands with everyone but himself, #1 AND #2, resulting in 7 handshakes. See the pattern? If you follow the pattern correctly, you get: 9+8+7+6+5+4+3+2+1=45 handshakes.

## 65 comments:

sfgsafg

I would write down the problem in a paper and solve it, instead of using calculator.

1) broken calculator:

458+548+354

You would have to put in:

448+448+344

You will have leftovers from the original number.Then you would add them, You should get: 1,240

You would take your answer and add the leftovers that you had from before. The leftovers are: 10 from 458, 100 from 548, 10 from 354. When you add them up you should get: 1,360. To check if it's correct you would add:458+548+354 on your calculator and you would then get: 1,360. If this doesn't make any sense sorry if it is confusing.

1.) BROKEN CALCULATOR:

Yes, there are more than one method to solve this problem. But what I think is the best is changing 50 or 500 to any numbers that can add up to that number. ( to make this easier, use friendly numbers like 30+20, 10+40,200+300 and 400+100 )

eg. 458+548+354

400+30+20+8= 458

458+200+300+40+8= 1,006

1006+300+20+30+4= 1,360.

2.) SHAKE HANDS:

We could solve this problem by using PROBABILITIES.

1) Broken calculator:

408 + 48 + 304 = 760

I am left with 50 + 500 + 50.

Using the calculator I will change the 50 to 20 + 30, and 500 to 200 + 300.

I already know two 50's make 100, so to make it easier I will add 60 + 40 to 200 + 300.

60 + 40 + 200 + 300 = 600.

Therefore, I just add 760 and 600 together which is equal to 1,360.

760 + 600 = 1,360.

Yes, there are more than one method to solve this, but for me this is the easier way.

2) Handshake:

For this problem, I can solve this using probability. To show you, you'd have to check my booklet.

calculator : to solve this .... I would do thiis .... instead of 458 + 548 + 354 , i would ddo. 400 + 30 + 20 + 8 ( 458 ) + 300 + 200 + 40 + 8 ( 548 ) + 300 + 30 + 20 + 4 ( 354 ) = 1360

handshake : you could some this using probability .

1.) Broken Calculator

What I did is like Marie's but i chose different numbers. 33 and 16If we use these numbers it would look like this:

400+33+16+8=458

330+160+40+8=548

300+33+16+4=354

If you add those up the sum would be 1,360.

2.) Handshake

We could use probabilities to solve this.

BROKEN CALCULATOR

If the key was broken, I would solve this problem by changing the question to 448+448+344, and add the sum of what I subtracted (to create the "new" question) to the answer of the question. (10+100+10=120=REMAINDERS) (ANSWER: 448+448+344=1,240+120=1,360) Yes, there is more than 1 way, but I "prefer" this way because I chose the number that is 1 less than 5, which makes it easier to add the remainders and the new question.

HANDSHAKE

Question: How many times can 10 people shake hands with eachother? The same two people shake hands only once. Can you find the pattern?

I made a chart and charted down the sample space for how many combinations, and crossed out the combonations that already have been written on the chart.

Answer: 10 people can shake hands with eachother 45 times. Yes, the pattern is that the amount of combos gets lower by 1, whenever you go up by 1 person.

EXAMPLE:

Person #1= 9 combos

Person #2= 8 combos

Person #3= 7 combos

(When I was done charting down the combonations, it looked like block of stairs.)

Sorry if it's hard to understand.

1. broken calculator

There is more than one method in solving this problem, but i find mine easier for myself.

(458)200+200+25+25+4+4

(548)250+250+20+20+4+4

(354)150+150+25+25+2+2

adding up all those numbers, will get my total of 1360. I have made doubles to figure out my answer.

2. Hand shake

You can use Probability to solve this problem

* change my '25+25s' to 20+30

* change my '250+250s' to 300+200

* change my 150+150s to 200+100

Question 1: Broken Calculator

Instead of adding 458+548+354. I would have added 408+448+344=1200. Then I would take the leftovers of the numbers then add the up (50+100+10=160). Then 1200+160= 1360

Question 2: Handshakes

I did a probability tree to solve this question and I got 90 different handshakes in total because each person shakes hands with 9 other people. So 9x10=90

BROKEN CALCULATOR:

The method I found easier, for me, was to change the numbers from 458+548+354 to 448+448+344. When added altogether it should add up to 1240. The leftovers from each number:10,10,100 should add together and equal 120.Afterward, I added the two numbers together and got 1360.

HANDSHAKE:

Can be solved by using probability. I organized my outcomes.Which looked like this:

1- 2,3,4,5,6,7,8,9,10

2- 3,4,5,6,7,8,9,10

3- 4,5,6,7,8,9,10

4- 5,6,7,8,9,10

5- 6,7,8,9,10

6- 7,8,9,10

7- 8,9,10

8- 9,10

9- 10

10-

So 10 people can shake hands with each other 45 times.

Problem 1: Broken Calculator

Yes, There will be more than one method to solve this problem. I solved this problem by changing the numbers. I took away 10 from 458 to equal 448. I took another 10 away from 354 to become 344. Then I took away 100 from 548 to give us 448. When you add our "new" numbers together it gives us a total of 1240. Now add the leftovers together, 10+10+100=120. Lastly add 1240+120 to equal 1360.

Problem 2- Handshake

I would solve this problem using probability. I would have to show you all my work. For this problem, I used a T-chart to organize all my numbers.

john 8-14

1.broken calculator:

458+548+354=?

change 458 to 460 then change 548 to 648 then change 354 to 360 - to 108=1360

2.handshake:

i will use probabilities to solve this

question.

Broken calculator:

I would add 458+548+354=1350

440+448+344=1232

8 +100+ 10=118

1232+118=1350

Hand shake:

I would use proboility for example

person 1 gets 9 hand shakes

Person 2 gets 8 hand shakes

person 3 gets 7 hand shakes

person 4 gets 6 hand shakes Etc.

1)broken calculator.

458+548+354

i have a another method to add this without using 5.

what I did was I changed the numbers and I got 408+48+304 so i added that and i got 760, but i still have 50,500,and 50 so what i did was I i i had to think of numbers to make that number so i went from 50 to 20+30 and 500 to 200+300, then I added 20+30+20+30+200+300 and I got 600 so after i added 600 and 760 and got 1360.

2)Hand shake

What i used here is probability.

1-2,3,4,5,6,7,8,9,10

2-3,4,5,6,7,8,9,10

3-4,5,6,7,8,9,10

4-5,6,7,8,9,10

5-6,7,8,9,10

6-7,8,9,10

7-8,9,10

8-9,10

9-10

10-

so the answer is 10 people can shake hands 45 times

It's so hard when you can't use the number 5 on the calculator. I wrote it on paper too, Windy.

Broken calculator:

What I did was, break it down and kind of used expanded form. It would be easier if you use friendly numbers.

eg.

400+40+10+8=458

300+200+40+8=548

300+30+20+4=354

So now I added them all up, the answer I got is 1,360.

Hand Shake:

This can be solve using probability.

I did my work in my notebook.

Broken Calculator:

I found this easier, for me, was to change the numbers from 458+548+354 to 448+448+344. When added i added it altogether it gave me 1240. the numbers that were left over from each number are :10,10,100 altogeather it gives me 120.then , I added the two numbers together and got 1360.

.

2)SHAKE HANDS. we can solve this problem by useing probibility.

"HANDSHAKE"

1st 9 shakehands

2nd 8 shakehands

3rd 7 shakehands

4th 6 shakehands

5th 5 shakehands

6th 4 shakehands

7th 3 shakehands

8th 2 shakehands

9th 1 shakehand

10th 0 shakehand

so all in all is 45

1) Broken Calculator:

458+548+354

Instead of having to add that, I found a method that was easy for me to do:

448+448+344

Now you have leftovers of the numbers, which are 10 from 458, 100 from 548 and 10 from 345. You then add them together:

10+10+100=120

448+448+344=1,240

120+1,240=1,360

2) Handshake

I solved the problem using probability. For me to organize the outcomes, I used a chart. And, the answer is that 10 people would shake hands with each other 45 times.

Yes there is more than 1 way. I took away ten on each number. So it would be..

448+448+344. You would get 1,240. Then you would get 10, 100, and 10 again. You add the leftovers, then you get 1,360.

Handshake: I used probability.

*Changed the 5 to 4. Not taking away 10

Broken Calculator:

first i would change 458 to 408, 548 to 48, 354 to 304. then I'll add them up and get: 760. then I'll add 50+500+50, we cant use 5' so ill change it to: 50 to 20+30, 500 to 200+300, then 50 to 20+30. add them up: 200+300+30+30+20+20=600. 600+760=1360

the answer is: 1360

Handshake:

this problem can be solved by using a probability chart.

Broken Calculator:

Original:458+548+354

Mine:408+48+304

I left out the 5's and so I was left with 50,500,and 50.So I tried making them even.500= 2+3=5 200+300=500 then the 50 will just be added to the other 50 which makes it 500.

Answer:408+48+304+200+300(500)+100(50+50)=1360

This is my answer.

1) Broken calculator :

458+548+354

You could've used the place values as your advantage

458 instead of doing that you could've put 400+20+30+8

548 you could've put 200+300+40+8

354 you could've put 300+20+30+4.

Instead of using the 5 in several place values think of numbers that will add up to the 5 on that place value and still have the answer.

400+20+30+8+

200+300+40+8+

300+20+30+4 =1 360

2)Shake Hands

To solve this problem you could use a Probabilty web or chart.

1)Broken Calculator:

If my calculator broke and I had the math problem 458+548+354 I would replace the 5's with 6 so that I could use my calculator to solve the problem.You will also have to subtract from the answer you get because your answer will be greater than the actual answer. You will have to subtract the amount you added to the question in the beginning which was 120.

Example:

468+648+364=1480

1480-120=1360

2)Shake Hands:

For question 2 I used probability. I organized my outcomes using a

T-table.

Example:

1- 2,3,4,5,6,7,8,9,10

2- 3,4,5,6,7,8,9,10

3- 4,5,6,7,8,9,10

4- 5,6,7,8,9,10

5- 6,7,8,9,10

6- 7,8,9,10

7- 8,9,10

8- 9,10

9- 10

10- 10 has already shaken hands with everyone.

10 people can shake hands with each other 45 times.

1. Broken Calculator

Instead of adding 458+548+354 I subtract 10 from 458, 100 from 548, and 10 from 354, which leads me to 448+448+344. It should be equvilent to 1 240. You then add 10+100+10 which we got from taking it away from 458+548+344. It should equal 120. After that add 120+1 240 and you get 1 360.

2. Handshake

To answer this, you would have to use a probability sample space, but you also have to ensure that to people do not shake hands more than twice(eg. 2,1 and 1,2) Each number represents one person.

(1,2) (2,3) (3,4) (4,5) (5,6) (6,7)

(1,3) (2,4) (3,5) (4,6) (5,7) (6,8)

(1,4) (2,5) (3,6) (4,7) (5,8) (6,9)

(1,5) (2,6) (3,7) (4,8)(5,9)(6,10)

(1,6) (2,7) (3,8) (4,9) (5,10)

(1,7) (2,8) (3,9) (4,10)

(1,8) (2,9) (3,10)

(1,9) (2,10)

(1,10)

=39 possibilities all together.

A pattern that I noticed is that the second digit will be one less than the one below it. Example,

1,2 <---

1,3 <--- 2,3,4.

1,4 <---

1) Broken calculater

458+548+354= 1360

S.S. If the 5 key on your calculater is broken the awnser is 1,360

O.A. 0 50,000

M.I. 400+400+300+58+54+148= 1,360

Yes there is more than 1 way to solve it. I like the way i did it best cause its easy.

2) Hand shaking

S.S. Ten people can shake hands forty four times.

O.A. 0 1000

M.I. #1 shakes hands with 9 people

#2 shakes hands with 8 people

#3 shakes hands with 7 people

#4 shakes hands with 6 people

#5 shakes hands with 5 people

#6 shakes hands with 4 people

#7 shakes hands with 3 people

#8 shakes hands with 2 people

#9 shakes hands with 1 person

The pattern is it goes 9,8,7,6,5,4,3,2,1

1) BROKEN CALCULATOR:

458+548+354

I know that there are many methods to solve this, but I chose the easiest one, and that is to just replace or fill up the numbers that are missing with other numbers except for five.

400+38+20= 458

400+100+48=548

200+100+48+6= 354

458+548+354= 1,360

2) I just used probabilities to solve it.

Broken Calculator:

I would solve this problem by just adding:

408 + 048 + 304

Which add up to: 760

I got this number by taking out the fives in the digit places so they become leftovers.

Now 50, 500, and 50 is left.

Change the 50's into 40 + 10 40 + 10 which equals to 100. Then add 400 + 100 + 100

Which equals to 600.

then add 760 + 600 =

1360

Handshake Problem:

For this problem you could use probability but I chose to use pictures.

For my answer I got 45 times 10 people can shake hands with each other.

1 broken calcaulator:

458+548+354

A) yes there is more than one way there is this

way where you would have to put this in

448+448+344 so you would

add that up and still remembering about the 10

10 100

left so i would ad those other numbers up

so it would be 1240 then adding the 5 from your

head it would be 1360.

B) i like having to use the 5 on the calculator

because it would make things more easier.

2 handshake:

i had wrote down my outcomes which looks like this:

1 2 3 4 5 6 7 8 9 10

1 3 3 5 5 7 7 9

1 4 3 6 58 7 10

1 5 3 7 59

1 6 3 8 5 10

1 7 3 9

1 8 3 10

1 9

1 10

2 3 4 5 6 7 8 9

2 4 4 6 6 8 8 10

2 5 4 7 6 9

2 6 4 8 6 10

2 7 4 9

2 8 4 10

2 9

2 10

1)BROKEN CALCULATOR: Since you cant use the five, you should just use the other numbers. Example: 1000+300+60,600+600+100+60 or 700+400+200+60. Then it will equal 1360.

2)SHAKING HANDS: For that question you would need probability.

Im sorry if i didnt do it right harbeck !

1. Broken calculator:

Yes there are more than one method. I would change 458+548+354 to 448+448+344. There are leftovers from the numbers so it should add up to: 1240. The leftover from each number:10,10,100would add and equal 120 so then i add 2 numbers to equal 1,360.

2. Handshakes

1 - 9 shakehands

2 - 8 shakehands

3 - 7 shakehands

4 - 6 shakehands

5 - 5 shakehands

6 - 4 shakehands

7 - 3 shakehands

8 - 2 shakehands

9 - 1 shakehand

10 - 0 shakehand

Broken Calculator:

458+548+354

I would do this:

400+40+10+8(458)400+100+40+8(548) 300+30+20+4(354)and you would get 1,360 all together.

BROKEN CALCULATOR

I wouldn't do 458 + 548 + 354 I would do 400, 30 + 20 + 8 which will be 458, 300 + 200 + 40 + 8 which will be 548, 300 + 30 + 20 + 4 is 354

All of them together will equal to 1360

HANDSHAKE:

I could solve this by using probabilities.

Broken Calculator:

458+548+354

For this problem I would replace the fives with fours then add the new numbers together.

448+448+344=1240

After that, add 10+100+10=120

1240+120=1360

Handshake:

For this problem I made a probability chart. I wrote down all the possible outcomes and then I took out the numbers that were already used. The answer I got was 45.

My chart looked like this:

12345678910

2345678910

345678910

45678910

5678910

678910

78910

8910

910

10

1) Broken Calculator:

458+584+354

I would do is put in:

408+84+304

Then i add them all up Got 796.

But I still left with 50,500,50.So i did was make them even like 200+300=500. Then the the 50 i just add both of them to make a 100.

Answer: 408+84+304+200+300(500)+50+50(100)=1.360

2)Handshake: I would solve it by using probability.

Broken Calculator:

What I did was subtract where I saw the number five. I subtracted 40 from 458 which made 418, then I subtracted 400 from 548 which made 148, and then I subtracted 40 from 354 which made 314. Then I added 418+148+314=880. Then I added 40+40+400=480. I added 880+480= 1360. That is one of the ways I used to figure out this question. I am sure there are more than one way to answer this question.

Hand shaking:

I used Probability. The first personn can shake hands with nine people, the second person eight, third seven, fourth sixth, fifth fifth, sixth fourth, seventh three, eighth two, nine one, and the tenth person already shook hands. So that would come down to ten people shaking hands forty five times.

1) broken calculator

You punch in 468+648+364 and the subtract 120 and you would get 1360.

2) hand shakes

Originally I got 55 but when I looked back at my answers the answer is 45.

For the hand shake one I used probability.

Broken calculator:

458+548+354, I multiplied the numbers by 2 then added them all up. Then i followed by dividing it by 2.

(458x2=916,548x2=1096,354x2=708

708+916+1096 = 2720/2 = 1360)

Handshake:

What I did was use probability to solve this. My answer ended up being 45, I got 45 because the first person can only shake hands with 9 people, the second can only shake with 8, third can only shake with 7, fourth can only shake with 6, fifth can shake with 5, sixth can shake with 4, seventh can shake with 3, eighth can shake with 2, ninth can shake with 1 and the tenth cant shake with anyone.

1) Broken Calculator:

I did the same thing as Bennette. (making friendly numbers so it would be easier to add)

Question: 458+548+354=?

400+40+10+8= 458.

200+300+40+8= 548.

300+20+30+4= 354.

Then add all the numbers together. & I know it seems like a lot of work, but you're still getting the answer. :)

1) Broken calculator

I did it this way:

408+48+304=760

Then I added 100 from the two 50s.

760+100=860

After, I added 200 and 300 to make the 500.

860+200+300=1360

My final answer is 1360. This to me was the easiest way.

2)Handshake

To solve this problem I used probability.

1 - 2,3,4,5,6,7,8,9,10 = 9 shakes

2 - 3,4,5,6,7,8,9,10 = 8 shakes

3 - 4,5,6,7,8,9,10 = 7 shakes

4 - 5,6,7,8,9,10 = 6 shakes

5 - 6,7,8,9,10 = 5 shakes

6 - 7,8,9,10 = 4 shakes

7 - 8,9,10 = 3 shakes

8 - 9,10 = 2 shakes

9 - 10 = 1 shake

Then add up all the shakes.

It all adds up to 45 shakes.

1) If the 5 key is broken on my calculator I would use this: 367+630+363

To get the answer of 1,360 and yes there are more than one way. The best way to me is to to change the 5's to any number and try to get close to the right number by changing other digits.

2) For the hand shakes I made this:

1-2,3,4,5,6,7,8,9,10

2-3,4,5,6,7,8,9,10

3-4,5,6,7,8,9,10

4-5,6,7,8,9,10

5-6,7,8,9,10

6-7,8,9,10

7-8,9,10

8-9,10

9-10

The sum of all shakes is 45 shakes. The pattern is that the number is getting less every time you hand shake someone.

1.Broken Calculator

I would turn all the 5's into 4's so the question would look like...

448+448+344=1240

I know that I had to subtract to change the 5's to 4's so now I must add those back. 10+100+10=120 and then I would add that to the first answer 1240+120= 1360

Another way it could be done is by changing the 5's into 6's so the question would look like 468+648+364=1480.

I added numbers to change the 5's to 6's so I would need to subtract them from the total. 10+100+10=120 1480-120=1360.

I like the first one better because it is easier to add than to subtract.

2. Shake Hands

There is a patter to figure it out. The first person will shake hands with another person 9 times and each person after that will shake hands 1 less time than the person before them. For a total of 45 handshakes between the 10 people.

Or you can use a chart

1 2 3 4 5 6 7 8 9 10

1 O $ $ $ $ $ $ $ $ $

2 X O $ $ $ $ $ $ $ $

3 X X O $ $ $ $ $ $ $

4 X X X O $ $ $ $ $ $

5 X X X X O $ $ $ $ $

6 X X X X X O $ $ $ $

7 X X X X X X O $ $ $

8 X X X X X X X O $ $

9 X X X X X X X X O $

10X X X X X X X X X O

$ - hand shake

X - have already shaken hands

O - you can't shake hands with yourself

1. Broken Calculator

458+548+354

I answered this by breaking up each number with 5 into smaller numbers. For example, I took, 500 and broke it into numbers like 200+300.

I answered it like this:

400+200+300+8+400+100+40+8+300+30+

20+4=1360

2.Handshake

I answered this by probability:

1. 1,2,3,4,5,6,7,8,9,10

2. 1,2,3,4,5,6,7,8,9

3. 1,2,3,4,5,6,7,8 etc.

well mine is like marilen's cause if you cant type 5 in the calculator you can just type like for example you want to type 500 you can type 300+200 instead in the calculator and ur not using the number "5".

Hand Shake:

well for me we can use probability too....

1) Broken calculator:

This way is only one way of doing it. First change every single 5 to a 4 so that you should have:

458+548+354 ----> 448+548+344

Now you add it, you should get 1240. Knowing you've changed every 5 to 4 now you just add 1, 10, or 100 depending on which place values you changed. In this case you should have 120 in total to add to 1240. You should get 1360.

2) Hand shake

In this problem you can use probability to answer it. Knowing that there are 10 people shake hands with each other, show who each person shakes hands with, example:

Person 1: 2,3,4,5,6,7,8,9,10

Person 2: 3,4,5,6,7,8,9,10

Person 3: 4,5,6,7,8,9,10

So if you get to the tenth person it would show that each person has shaken hands with one another. In total 10 people can shake 45 times.

1)broken calculator:458+548+354

you need to subtract:

458 by 10

548 by 100

448 by 10

the problem would then be 448+448+344+120=1360

2)shake hands:

I used probability do do this problem.

A)BROKEN CALCULATOR:

First, find every number's place value.Then, when every value of 5 is all revealed, change it addends that don't require 5(use happy numbers) and when is summed up, it is equal to the value of five. Lastly, add them all up in the normal way.

458+548+354=

1)400+50+8+500+40+8+300+50+4=

2)400+(30+20)+8+(300+200)+40+8+300+(30+20)+4=

3)400+(30+20)+8+(300+200)+40+8+300+(30+20)+4=1,360

B)Handshake:

This problem is to be solved by using Probabilities.

If it doesn't make sense, I apologize and I'm sorry I posted it late, we had internet problems last night.

1)Broken Calculator

What I did to solve this problem was rewriting the question to:

448+448+344=1240

Then I added the numbers that I took away.

10+100+10=120

Then I added 1240 and 120. The total I got was 1360.

2) Handshake

To solve this problem, you could use probability. I wrote out my outcomes like this.

1- 2,3,4,5,6,7,8,9,10

2- 3,4,5,6,7,8,9,10

3- 4,5,6,7,8,9,10

4- 5,6,7,8,9,10

5- 6,7,8,9,10

6- 7,8,9,10

7- 8,9,10

8- 9,10

9- 10

10-

So 10 people can shake hands 45 times.

For the calculator instad of typing in 458+548+354 I would type in 408+20+30+200+300+48+304+20+30 this way can be reapeted with ervery number up to 5.

For the handshake every person would get a number from 1to10 and everyone shakes hands with ten then everyone exept 10 shakes hands with 9 and so on and that would be the pattern and the answer would be 45.

1)broken calculator:

458+548+354

You would have to put:

448+448+344=1,240

Now the remaining numbers would be 10 from 458, 100 from 548, 10 from 354. Add them up and u get 120.

120+1240=1,360.

1 - The Broken Calculator

To solve this problem, I would add the first and last numbers first - I would add 10 to the first number and subtract 10 to the last number, eliminating the need for the five key.

eg 468+344=812

To add the remaining number, I would add 100 to it first, then subtract 100 from the total, again eliminating the using of the five key.

eg 812+648=1460-100=1360,the answer.

There are other ways to do this problem, but this is my favourite.

2 - The Handshake

If you think correctly, person #1

can shake hands with everyone but himself, resulting in nine handshakes. Person #2 can shake hands with everyone except himself AND #1, resulting in 8 handshakes. Person #3 can shake hands with everyone but himself, #1 AND #2, resulting in 7 handshakes.

See the pattern?

If you follow the pattern correctly, you get:

9+8+7+6+5+4+3+2+1=45 handshakes.

1-2,3,4,5,6,7,8,9,10

2-3,4,5,6,7,8,9,10

3-4,5,6,7,8,9,10

4-5,6,7,8,9,10

5-6,7,8,9,10

6-7,8,9,10

7-8,9,10

8-9,10

9-10

10-

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