Opal, Yen and Linda had a total of 163 stamps. The ratio of Yen's stamps to Linda's stamps was at first 8 : 3. After Opal and Yen each gave half of their stamps away, the 3 children had 98 stamps left. How many stamps did Opal and Yen have at first?
| |
Opal |
Yen |
Linda |
Total |
| Before |
2 p |
8 u |
3 u |
163 |
| Change |
- 1 p |
- 4 u |
|
- 65 |
| After |
1 p |
4 u |
3 u |
98 |
Number of stamps that Opal and Yen gave away
= 163 - 98
= 65
1 p + 4 u = 65
1 p = 65 - 4 u --- (1)
1 p + 4 u + 3 u = 98
1 p + 7 u = 98
1 p = 98 - 7 u --- (2)
(1) = (2)
65 - 4 u = 98 - 7 u
7 u - 4 u = 98 - 65
3 u = 33
1 u = 33 ÷ 3 = 11
From (1)
1 p = 65 - 4 u
1 p = 65 - 4 x 11
1 p = 65 - 44 = 21
Number of stamps that Opal and Yen had at first
= 2 p + 8 u
= 2 x 21 + 8 x 11
= 42 + 33
= 75
Answer(s): 75
