Luke, Paul and Cole had a total of 92 stamps. The ratio of the number of stamps that Paul had to the number of stamps that Cole had was 4 : 7. After Luke and Paul each gave away half of their stamps, the 3 children had 74 stamps left. How many stamps did Paul and Cole have in the end?
| |
Luke |
Paul |
Cole |
Total |
| Before |
2 p |
4 u |
7 u |
92 |
| Change |
- 1 p |
- 2 u |
|
- 18 |
| After |
1 p |
2 u |
7 u |
74 |
Total number of stamps that Luke and Paul gave away
= 92 - 74
= 18
1 p + 2 u = 18 --- (1)
1 p + 2 u + 7 u = 74
1 p + 9 u = 74 --- (2)
(2) - (1)
(1 p + 9 u) - (1 p + 2 u) = 74 - 18
9 u - 2 u = 56
7 u = 56
1 u = 56 ÷ 7 = 8
Total number of stamps that Paul and Cole had in the end
= 2 u + 7 u
= 9 u
= 9 x 8
= 72
Answer(s): 72
