The ratio of Cindy's money to Elyse's money was 1 : 2. After Cindy spent four times as much as Elyse, Cindy and Elyse had $8 and $37 left respectively. Find the amount of money each of the girls have at first.
- Cindy
- Elyse
| |
Make u the same
(1)x2 = (3) |
Cindy
(1) |
Elyse
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 8 p |
- 4 p |
- 1 p |
| After |
16 |
8 |
37 |
(a)
1 u - 4 p = 8
2 u = 8 + 4 p --- (1)
2 u - 1 p = 37
2 u = 37 + 1 p --- (2)
(1)
x2
2 u = 16 + 8 p --- (3)
(3) = (2)
16 + 8 p = 37 + 1 p
8 p - 1 p = 37 - 16
7 p = 21
1 p = 21 ÷ 7 = 3
Amount that Cindy had at first
= 8 + 4 p
= 8 + 4 x 3
= 8 + 12
= $20
(b)
Amount that Elyse had at first
= 16 + 8 p
= 16 + 8 x 3
= 16 + 24
= $40
Answer(s): (a) $20; (b) $40
