Luis, Ahmad and Cody had a total of 112 erasers. The ratio of the number of erasers that Ahmad had to the number of erasers that Cody had was 6 : 7. After Luis and Ahmad each gave away half of their erasers, the 3 children had 84 erasers left. How many erasers did Ahmad and Cody have in the end?
| |
Luis |
Ahmad |
Cody |
Total |
| Before |
2 p |
6 u |
7 u |
112 |
| Change |
- 1 p |
- 3 u |
|
- 28 |
| After |
1 p |
3 u |
7 u |
84 |
Total number of erasers that Luis and Ahmad gave away
= 112 - 84
= 28
1 p + 3 u = 28 --- (1)
1 p + 3 u + 7 u = 84
1 p + 10 u = 84 --- (2)
(2) - (1)
(1 p + 10 u) - (1 p + 3 u) = 84 - 28
10 u - 3 u = 56
7 u = 56
1 u = 56 ÷ 7 = 8
Total number of erasers that Ahmad and Cody had in the end
= 3 u + 7 u
= 10 u
= 10 x 8
= 80
Answer(s): 80
