The ratio of Wendy's money to Joelle's money was 1 : 3. After Wendy spent four times as much as Joelle, Wendy and Joelle had $7 and $54 left respectively. Find the amount of money each of the girls have at first.
- Wendy
- Joelle
| |
Make u the same
(1)x3 = (3) |
Wendy
(1) |
Joelle
(2) |
| Before |
3 u |
1 u |
3 u |
| Change |
- 12 p |
- 4 p |
- 1 p |
| After |
21 |
7 |
54 |
(a)
1 u - 4 p = 7
3 u = 7 + 4 p --- (1)
3 u - 1 p = 54
3 u = 54 + 1 p --- (2)
(1)
x3
3 u = 21 + 12 p --- (3)
(3) = (2)
21 + 12 p = 54 + 1 p
12 p - 1 p = 54 - 21
11 p = 33
1 p = 33 ÷ 11 = 3
Amount that Wendy had at first
= 7 + 4 p
= 7 + 4 x 3
= 7 + 12
= $19
(b)
Amount that Joelle had at first
= 21 + 12 p
= 21 + 12 x 3
= 21 + 36
= $57
Answer(s): (a) $19; (b) $57
