Ivan, Xavier and Asher had a total of 110 stamps. The ratio of the number of stamps that Xavier had to the number of stamps that Asher had was 8 : 9. After Ivan and Xavier each gave away half of their stamps, the 3 children had 82 stamps left. How many stamps did Xavier and Asher have at first?
| |
Ivan |
Xavier |
Asher |
Total |
| Before |
2 p |
8 u |
9 u |
110 |
| Change |
- 1 p |
- 4 u |
|
- 28 |
| After |
1 p |
4 u |
9 u |
82 |
Total number of stamps that Ivan and Xavier gave away
= 110 - 82
= 28
1 p + 4 u = 28 --- (1)
1 p + 4 u + 9 u = 82
1 p + 13 u = 82 --- (2)
(2) - (1)
(1 p + 13 u) - (1 p + 4 u) = 82 - 28
13 u - 4 u = 54
9 u = 54
1 u = 54 ÷ 9 = 6
Total number of stamps that Xavier and Asher had at first
= 8 u + 9 u
= 17 u
= 17 x 6
= 102
Answer(s): 102
