Ivan, Julian and Justin shared a bag of erasers. Julian took 27 as many erasers as Justin. Ivan took twice as many erasers as the total Julian and Justin took. After Ivan had given 32 to Julian and 4 to Justin, Julian gave 4 to Justin. In the end, all three of them had the same number of erasers. Find the difference between the number of erasers that Ivan and Julian had at first.
| |
Julian |
Justin |
Ivan |
Total |
| Before |
2 u |
7 u |
18 u |
27 u |
| Change 1 |
+ 32 |
|
- 32 |
|
| Change 2 |
|
+ 4 |
- 4 |
|
| Change 3 |
- 4 |
+ 4 |
|
|
| After |
1x9 =
9 u |
1x9 =
9 u |
1x9 =
9 u |
3x9 =
27 u |
Total number of erasers that Julian and Justin had at first
= 2 u + 7 u
= 9 u
Number of erasers that Ivan had at first
= 2 x 9 u
= 18 u
The total number of erasers remains unchanged. Make the total number of erasers the same. LCM of 3 and 27 is 27.
Number of erasers that Justin received from Julian and Ivan
= 9 u - 7 u
= 2 u
2 u = 4 + 4
2 u = 8
1 u = 8 ÷ 2 = 4
Difference between the number erasers that Ivan and Julian had at first
= 18 u - 2 u
= 16 u
= 16 x 4
= 64
Answer(s): 64
