Jack, Justin and Asher shared a bag of buttons. Justin took 25 as many buttons as Asher. Jack took twice as many buttons as the total Justin and Asher took. After Jack had given 34 to Justin and 8 to Asher, Justin gave 4 to Asher. In the end, all three of them had the same number of buttons. Find the difference between the number of buttons that Jack and Justin had at first.
| |
Justin |
Asher |
Jack |
Total |
| Before |
2 u |
5 u |
14 u |
21 u |
| Change 1 |
+ 34 |
|
- 34 |
|
| Change 2 |
|
+ 8 |
- 8 |
|
| Change 3 |
- 4 |
+ 4 |
|
|
| After |
1x7 =
7 u |
1x7 =
7 u |
1x7 =
7 u |
3x7 =
21 u |
Total number of buttons that Justin and Asher had at first
= 2 u + 5 u
= 7 u
Number of buttons that Jack had at first
= 2 x 7 u
= 14 u
The total number of buttons remains unchanged. Make the total number of buttons the same. LCM of 3 and 21 is 21.
Number of buttons that Asher received from Justin and Jack
= 7 u - 5 u
= 2 u
2 u = 8 + 4
2 u = 12
1 u = 12 ÷ 2 = 6
Difference between the number buttons that Jack and Justin had at first
= 14 u - 2 u
= 12 u
= 12 x 6
= 72
Answer(s): 72
