The ratio of Min's money to Cindy's money was 1 : 3. After Min spent thrice as much as Cindy, Min and Cindy had $8 and $40 left respectively. Find the amount of money each of the girls have at first.
- Min
- Cindy
| |
Make u the same
(1)x3 = (3) |
Min
(1) |
Cindy
(2) |
| Before |
3 u |
1 u |
3 u |
| Change |
- 9 p |
- 3 p |
- 1 p |
| After |
24 |
8 |
40 |
(a)
1 u - 3 p = 8
3 u = 8 + 3 p --- (1)
3 u - 1 p = 40
3 u = 40 + 1 p --- (2)
(1)
x3
3 u = 24 + 9 p --- (3)
(3) = (2)
24 + 9 p = 40 + 1 p
9 p - 1 p = 40 - 24
8 p = 16
1 p = 16 ÷ 8 = 2
Amount that Min had at first
= 8 + 3 p
= 8 + 3 x 2
= 8 + 6
= $14
(b)
Amount that Cindy had at first
= 24 + 9 p
= 24 + 9 x 2
= 24 + 18
= $42
Answer(s): (a) $14; (b) $42
