Erika, Rachel and Winnie had a total of 73 erasers. The ratio of Rachel's erasers to Winnie's erasers was at first 8 : 3. After Erika and Rachel each gave half of their erasers away, the 3 children had 41 erasers left. How many erasers did Erika and Rachel have at first?
| |
Erika |
Rachel |
Winnie |
Total |
| Before |
2 p |
8 u |
3 u |
73 |
| Change |
- 1 p |
- 4 u |
|
- 32 |
| After |
1 p |
4 u |
3 u |
41 |
Number of erasers that Erika and Rachel gave away
= 73 - 41
= 32
1 p + 4 u = 32
1 p = 32 - 4 u --- (1)
1 p + 4 u + 3 u = 41
1 p + 7 u = 41
1 p = 41 - 7 u --- (2)
(1) = (2)
32 - 4 u = 41 - 7 u
7 u - 4 u = 41 - 32
3 u = 9
1 u = 9 ÷ 3 = 3
From (1)
1 p = 32 - 4 u
1 p = 32 - 4 x 3
1 p = 32 - 12 = 20
Number of erasers that Erika and Rachel had at first
= 2 p + 8 u
= 2 x 20 + 8 x 3
= 40 + 9
= 49
Answer(s): 49
