Seth, Jack and Valen had a total of 120 erasers. The ratio of the number of erasers that Jack had to the number of erasers that Valen had was 4 : 7. After Seth and Jack each gave away half of their erasers, the 3 children had 95 erasers left. How many erasers did Jack and Valen have at first?
| |
Seth |
Jack |
Valen |
Total |
| Before |
2 p |
4 u |
7 u |
120 |
| Change |
- 1 p |
- 2 u |
|
- 25 |
| After |
1 p |
2 u |
7 u |
95 |
Total number of erasers that Seth and Jack gave away
= 120 - 95
= 25
1 p + 2 u = 25 --- (1)
1 p + 2 u + 7 u = 95
1 p + 9 u = 95 --- (2)
(2) - (1)
(1 p + 9 u) - (1 p + 2 u) = 95 - 25
9 u - 2 u = 70
7 u = 70
1 u = 70 ÷ 7 = 10
Total number of erasers that Jack and Valen had at first
= 4 u + 7 u
= 11 u
= 11 x 10
= 110
Answer(s): 110
