The ratio of Gabby's money to Cindy's money was 1 : 4. After Gabby spent four times as much as Cindy, Gabby and Cindy had $4 and $46 left respectively. Find the amount of money each of the girls have at first.
- Gabby
- Cindy
|
Make u the same (1)x4 = (3) |
Gabby (1) |
Cindy (2) |
Before |
4 u |
1 u |
4 u |
Change |
- 16 p |
- 4 p |
- 1 p |
After |
16 |
4 |
46 |
(a)
1 u - 4 p = 4
4 u = 4 + 4 p --- (1)
4 u - 1 p = 46
4 u = 46 + 1 p --- (2)
(1)
x4
4 u = 16 + 16 p --- (3)
(3) = (2)
16 + 16 p = 46 + 1 p
16 p - 1 p = 46 - 16
15 p = 30
1 p = 30 ÷ 15 = 2
Amount that Gabby had at first
= 4 + 4 p
= 4 + 4 x 2
= 4 + 8
= $12
(b)
Amount that Cindy had at first
= 16 + 16 p
= 16 + 16 x 2
= 16 + 32
= $48
Answer(s): (a) $12; (b) $48