Valen, Asher and Brandon shared a bag of erasers. Asher took 35 as many erasers as Brandon. Valen took twice as many erasers as the total Asher and Brandon took. After Valen had given 38 to Asher and 10 to Brandon, Asher gave 8 to Brandon. In the end, all three of them had the same number of erasers. Find the difference between the number of erasers that Valen and Asher had at first.
| |
Asher |
Brandon |
Valen |
Total |
| Before |
3 u |
5 u |
16 u |
24 u |
| Change 1 |
+ 38 |
|
- 38 |
|
| Change 2 |
|
+ 10 |
- 10 |
|
| Change 3 |
- 8 |
+ 8 |
|
|
| After |
1x8 =
8 u |
1x8 =
8 u |
1x8 =
8 u |
3x8 =
24 u |
Total number of erasers that Asher and Brandon had at first
= 3 u + 5 u
= 8 u
Number of erasers that Valen had at first
= 2 x 8 u
= 16 u
The total number of erasers remains unchanged. Make the total number of erasers the same. LCM of 3 and 24 is 24.
Number of erasers that Brandon received from Asher and Valen
= 8 u - 5 u
= 3 u
3 u = 10 + 8
3 u = 18
1 u = 18 ÷ 3 = 6
Difference between the number erasers that Valen and Asher had at first
= 16 u - 3 u
= 13 u
= 13 x 6
= 78
Answer(s): 78
