Luke, Neave and Archie had a total of 67 stamps. The ratio of the number of stamps that Neave had to the number of stamps that Archie had was 2 : 9. After Luke and Neave each gave away half of their stamps, the 3 children had 56 stamps left. How many stamps did Neave and Archie have at first?
| |
Luke |
Neave |
Archie |
Total |
| Before |
2 p |
2 u |
9 u |
67 |
| Change |
- 1 p |
- 1 u |
|
- 11 |
| After |
1 p |
1 u |
9 u |
56 |
Total number of stamps that Luke and Neave gave away
= 67 - 56
= 11
1 p + 1 u = 11 --- (1)
1 p + 1 u + 9 u = 56
1 p + 10 u = 56 --- (2)
(2) - (1)
(1 p + 10 u) - (1 p + 1 u) = 56 - 11
10 u - 1 u = 45
9 u = 45
1 u = 45 ÷ 9 = 5
Total number of stamps that Neave and Archie had at first
= 2 u + 9 u
= 11 u
= 11 x 5
= 55
Answer(s): 55
