Ethan, Valen and Tommy had a total of 112 erasers. The ratio of the number of erasers that Valen had to the number of erasers that Tommy had was 4 : 7. After Ethan and Valen each gave away half of their erasers, the 3 children had 84 erasers left. How many erasers did Valen and Tommy have at first?
| |
Ethan |
Valen |
Tommy |
Total |
| Before |
2 p |
4 u |
7 u |
112 |
| Change |
- 1 p |
- 2 u |
|
- 28 |
| After |
1 p |
2 u |
7 u |
84 |
Total number of erasers that Ethan and Valen gave away
= 112 - 84
= 28
1 p + 2 u = 28 --- (1)
1 p + 2 u + 7 u = 84
1 p + 9 u = 84 --- (2)
(2) - (1)
(1 p + 9 u) - (1 p + 2 u) = 84 - 28
9 u - 2 u = 56
7 u = 56
1 u = 56 ÷ 7 = 8
Total number of erasers that Valen and Tommy had at first
= 4 u + 7 u
= 11 u
= 11 x 8
= 88
Answer(s): 88
