The ratio of Cindy's money to Rachel's money was 1 : 2. After Cindy spent four times as much as Rachel, Cindy and Rachel had $7 and $35 left respectively. Find the amount of money each of the girls have at first.
- Cindy
- Rachel
| |
Make u the same
(1)x2 = (3) |
Cindy
(1) |
Rachel
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 8 p |
- 4 p |
- 1 p |
| After |
14 |
7 |
35 |
(a)
1 u - 4 p = 7
2 u = 7 + 4 p --- (1)
2 u - 1 p = 35
2 u = 35 + 1 p --- (2)
(1)
x2
2 u = 14 + 8 p --- (3)
(3) = (2)
14 + 8 p = 35 + 1 p
8 p - 1 p = 35 - 14
7 p = 21
1 p = 21 ÷ 7 = 3
Amount that Cindy had at first
= 7 + 4 p
= 7 + 4 x 3
= 7 + 12
= $19
(b)
Amount that Rachel had at first
= 14 + 8 p
= 14 + 8 x 3
= 14 + 24
= $38
Answer(s): (a) $19; (b) $38
