Jen, Abi and Joelle had a total of 157 erasers. The ratio of Abi's erasers to Joelle's erasers was at first 10 : 3. After Jen and Abi each gave half of their erasers away, the 3 children had 92 erasers left. How many erasers did Jen and Abi have at first?
| |
Jen |
Abi |
Joelle |
Total |
| Before |
2 p |
10 u |
3 u |
157 |
| Change |
- 1 p |
- 5 u |
|
- 65 |
| After |
1 p |
5 u |
3 u |
92 |
Number of erasers that Jen and Abi gave away
= 157 - 92
= 65
1 p + 5 u = 65
1 p = 65 - 5 u --- (1)
1 p + 5 u + 3 u = 92
1 p + 8 u = 92
1 p = 92 - 8 u --- (2)
(1) = (2)
65 - 5 u = 92 - 8 u
8 u - 5 u = 92 - 65
3 u = 27
1 u = 27 ÷ 3 = 9
From (1)
1 p = 65 - 5 u
1 p = 65 - 5 x 9
1 p = 65 - 45 = 20
Number of erasers that Jen and Abi had at first
= 2 p + 10 u
= 2 x 20 + 10 x 9
= 40 + 27
= 67
Answer(s): 67
