Seth, Archie and Eric had a total of 122 erasers. The ratio of the number of erasers that Archie had to the number of erasers that Eric had was 8 : 5. After Seth and Archie each gave away half of their erasers, the 3 children had 81 erasers left. How many erasers did Archie and Eric have at first?
| |
Seth |
Archie |
Eric |
Total |
| Before |
2 p |
8 u |
5 u |
122 |
| Change |
- 1 p |
- 4 u |
|
- 41 |
| After |
1 p |
4 u |
5 u |
81 |
Total number of erasers that Seth and Archie gave away
= 122 - 81
= 41
1 p + 4 u = 41 --- (1)
1 p + 4 u + 5 u = 81
1 p + 9 u = 81 --- (2)
(2) - (1)
(1 p + 9 u) - (1 p + 4 u) = 81 - 41
9 u - 4 u = 40
5 u = 40
1 u = 40 ÷ 5 = 8
Total number of erasers that Archie and Eric had at first
= 8 u + 5 u
= 13 u
= 13 x 8
= 104
Answer(s): 104
