The ratio of Cindy's money to Jean's money was 1 : 4. After Cindy spent thrice as much as Jean, Cindy and Jean had $6 and $46 left respectively. Find the amount of money each of the girls have at first.
- Cindy
- Jean
| |
Make u the same
(1)x4 = (3) |
Cindy
(1) |
Jean
(2) |
| Before |
4 u |
1 u |
4 u |
| Change |
- 12 p |
- 3 p |
- 1 p |
| After |
24 |
6 |
46 |
(a)
1 u - 3 p = 6
4 u = 6 + 3 p --- (1)
4 u - 1 p = 46
4 u = 46 + 1 p --- (2)
(1)
x4
4 u = 24 + 12 p --- (3)
(3) = (2)
24 + 12 p = 46 + 1 p
12 p - 1 p = 46 - 24
11 p = 22
1 p = 22 ÷ 11 = 2
Amount that Cindy had at first
= 6 + 3 p
= 6 + 3 x 2
= 6 + 6
= $12
(b)
Amount that Jean had at first
= 24 + 12 p
= 24 + 12 x 2
= 24 + 24
= $48
Answer(s): (a) $12; (b) $48
