The ratio of Joelle's money to Xylia's money was 1 : 4. After Joelle spent four times as much as Xylia, Joelle and Xylia had $7 and $58 left respectively. Find the amount of money each of the girls have at first.
- Joelle
- Xylia
| |
Make u the same
(1)x4 = (3) |
Joelle
(1) |
Xylia
(2) |
| Before |
4 u |
1 u |
4 u |
| Change |
- 16 p |
- 4 p |
- 1 p |
| After |
28 |
7 |
58 |
(a)
1 u - 4 p = 7
4 u = 7 + 4 p --- (1)
4 u - 1 p = 58
4 u = 58 + 1 p --- (2)
(1)
x4
4 u = 28 + 16 p --- (3)
(3) = (2)
28 + 16 p = 58 + 1 p
16 p - 1 p = 58 - 28
15 p = 30
1 p = 30 ÷ 15 = 2
Amount that Joelle had at first
= 7 + 4 p
= 7 + 4 x 2
= 7 + 8
= $15
(b)
Amount that Xylia had at first
= 28 + 16 p
= 28 + 16 x 2
= 28 + 32
= $60
Answer(s): (a) $15; (b) $60
