Sabrina, Eva and Cathy had a total of 117 stamps. The ratio of Eva's stamps to Cathy's stamps was at first 10 : 3. After Sabrina and Eva each gave half of their stamps away, the 3 children had 69 stamps left. How many stamps did Sabrina and Eva have at first?
| |
Sabrina |
Eva |
Cathy |
Total |
| Before |
2 p |
10 u |
3 u |
117 |
| Change |
- 1 p |
- 5 u |
|
- 48 |
| After |
1 p |
5 u |
3 u |
69 |
Number of stamps that Sabrina and Eva gave away
= 117 - 69
= 48
1 p + 5 u = 48
1 p = 48 - 5 u --- (1)
1 p + 5 u + 3 u = 69
1 p + 8 u = 69
1 p = 69 - 8 u --- (2)
(1) = (2)
48 - 5 u = 69 - 8 u
8 u - 5 u = 69 - 48
3 u = 21
1 u = 21 ÷ 3 = 7
From (1)
1 p = 48 - 5 u
1 p = 48 - 5 x 7
1 p = 48 - 35 = 13
Number of stamps that Sabrina and Eva had at first
= 2 p + 10 u
= 2 x 13 + 10 x 7
= 26 + 21
= 47
Answer(s): 47
