Tom, Ivan and Zane had a total of 52 stamps. The ratio of the number of stamps that Ivan had to the number of stamps that Zane had was 8 : 7. After Tom and Ivan each gave away half of their stamps, the 3 children had 33 stamps left. How many stamps did Ivan and Zane have at first?
| |
Tom |
Ivan |
Zane |
Total |
| Before |
2 p |
8 u |
7 u |
52 |
| Change |
- 1 p |
- 4 u |
|
- 19 |
| After |
1 p |
4 u |
7 u |
33 |
Total number of stamps that Tom and Ivan gave away
= 52 - 33
= 19
1 p + 4 u = 19 --- (1)
1 p + 4 u + 7 u = 33
1 p + 11 u = 33 --- (2)
(2) - (1)
(1 p + 11 u) - (1 p + 4 u) = 33 - 19
11 u - 4 u = 14
7 u = 14
1 u = 14 ÷ 7 = 2
Total number of stamps that Ivan and Zane had at first
= 8 u + 7 u
= 15 u
= 15 x 2
= 30
Answer(s): 30
