Brandon, Michael and Nick had a total of 157 stamps. The ratio of the number of stamps that Michael had to the number of stamps that Nick had was 4 : 9. After Brandon and Michael each gave away half of their stamps, the 3 children had 128 stamps left. How many stamps did Michael and Nick have at first?
| |
Brandon |
Michael |
Nick |
Total |
| Before |
2 p |
4 u |
9 u |
157 |
| Change |
- 1 p |
- 2 u |
|
- 29 |
| After |
1 p |
2 u |
9 u |
128 |
Total number of stamps that Brandon and Michael gave away
= 157 - 128
= 29
1 p + 2 u = 29 --- (1)
1 p + 2 u + 9 u = 128
1 p + 11 u = 128 --- (2)
(2) - (1)
(1 p + 11 u) - (1 p + 2 u) = 128 - 29
11 u - 2 u = 99
9 u = 99
1 u = 99 ÷ 9 = 11
Total number of stamps that Michael and Nick had at first
= 4 u + 9 u
= 13 u
= 13 x 11
= 143
Answer(s): 143
