The ratio of Joelle's money to Cindy's money was 1 : 2. After Joelle spent five times as much as Cindy, Joelle and Cindy had $8 and $43 left respectively. Find the amount of money each of the girls have at first.
- Joelle
- Cindy
|
Make u the same (1)x2 = (3) |
Joelle (1) |
Cindy (2) |
Before |
2 u |
1 u |
2 u |
Change |
- 10 p |
- 5 p |
- 1 p |
After |
16 |
8 |
43 |
(a)
1 u - 5 p = 8
2 u = 8 + 5 p --- (1)
2 u - 1 p = 43
2 u = 43 + 1 p --- (2)
(1)
x2
2 u = 16 + 10 p --- (3)
(3) = (2)
16 + 10 p = 43 + 1 p
10 p - 1 p = 43 - 16
9 p = 27
1 p = 27 ÷ 9 = 3
Amount that Joelle had at first
= 8 + 5 p
= 8 + 5 x 3
= 8 + 15
= $23
(b)
Amount that Cindy had at first
= 16 + 10 p
= 16 + 10 x 3
= 16 + 30
= $46
Answer(s): (a) $23; (b) $46