The ratio of Min's money to Jean's money was 1 : 3. After Min spent thrice as much as Jean, Min and Jean had $7 and $37 left respectively. Find the amount of money each of the girls have at first.
- Min
- Jean
| |
Make u the same
(1)x3 = (3) |
Min
(1) |
Jean
(2) |
| Before |
3 u |
1 u |
3 u |
| Change |
- 9 p |
- 3 p |
- 1 p |
| After |
21 |
7 |
37 |
(a)
1 u - 3 p = 7
3 u = 7 + 3 p --- (1)
3 u - 1 p = 37
3 u = 37 + 1 p --- (2)
(1)
x3
3 u = 21 + 9 p --- (3)
(3) = (2)
21 + 9 p = 37 + 1 p
9 p - 1 p = 37 - 21
8 p = 16
1 p = 16 ÷ 8 = 2
Amount that Min had at first
= 7 + 3 p
= 7 + 3 x 2
= 7 + 6
= $13
(b)
Amount that Jean had at first
= 21 + 9 p
= 21 + 9 x 2
= 21 + 18
= $39
Answer(s): (a) $13; (b) $39
