Warren, Ken and Jack shared a bag of buttons. Ken took 37 as many buttons as Jack. Warren took twice as many buttons as the total Ken and Jack took. After Warren had given 58 to Ken and 22 to Jack, Ken gave 2 to Jack. In the end, all three of them had the same number of buttons. Find the difference between the number of buttons that Warren and Ken had at first.
| |
Ken |
Jack |
Warren |
Total |
| Before |
3 u |
7 u |
20 u |
30 u |
| Change 1 |
+ 58 |
|
- 58 |
|
| Change 2 |
|
+ 22 |
- 22 |
|
| Change 3 |
- 2 |
+ 2 |
|
|
| After |
1x10 =
10 u |
1x10 =
10 u |
1x10 =
10 u |
3x10 =
30 u |
Total number of buttons that Ken and Jack had at first
= 3 u + 7 u
= 10 u
Number of buttons that Warren had at first
= 2 x 10 u
= 20 u
The total number of buttons remains unchanged. Make the total number of buttons the same. LCM of 3 and 30 is 30.
Number of buttons that Jack received from Ken and Warren
= 10 u - 7 u
= 3 u
3 u = 22 + 2
3 u = 24
1 u = 24 ÷ 3 = 8
Difference between the number buttons that Warren and Ken had at first
= 20 u - 3 u
= 17 u
= 17 x 8
= 136
Answer(s): 136
