Liam, Julian and Justin shared a bag of buttons. Julian took 37 as many buttons as Justin. Liam took twice as many buttons as the total Julian and Justin took. After Liam had given 72 to Julian and 18 to Justin, Julian gave 9 to Justin. In the end, all three of them had the same number of buttons. Find the difference between the number of buttons that Liam and Julian had at first.
| |
Julian |
Justin |
Liam |
Total |
| Before |
3 u |
7 u |
20 u |
30 u |
| Change 1 |
+ 72 |
|
- 72 |
|
| Change 2 |
|
+ 18 |
- 18 |
|
| Change 3 |
- 9 |
+ 9 |
|
|
| After |
1x10 =
10 u |
1x10 =
10 u |
1x10 =
10 u |
3x10 =
30 u |
Total number of buttons that Julian and Justin had at first
= 3 u + 7 u
= 10 u
Number of buttons that Liam 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 Justin received from Julian and Liam
= 10 u - 7 u
= 3 u
3 u = 18 + 9
3 u = 27
1 u = 27 ÷ 3 = 9
Difference between the number buttons that Liam and Julian had at first
= 20 u - 3 u
= 17 u
= 17 x 9
= 153
Answer(s): 153
