The ratio of Raeann's money to Xandra's money was 1 : 2. After Raeann spent thrice as much as Xandra, Raeann and Xandra had $9 and $58 left respectively. Find the amount of money each of the girls have at first.
- Raeann
- Xandra
| |
Make u the same
(1)x2 = (3) |
Raeann
(1) |
Xandra
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 6 p |
- 3 p |
- 1 p |
| After |
18 |
9 |
58 |
(a)
1 u - 3 p = 9
2 u = 9 + 3 p --- (1)
2 u - 1 p = 58
2 u = 58 + 1 p --- (2)
(1)
x2
2 u = 18 + 6 p --- (3)
(3) = (2)
18 + 6 p = 58 + 1 p
6 p - 1 p = 58 - 18
5 p = 40
1 p = 40 ÷ 5 = 8
Amount that Raeann had at first
= 9 + 3 p
= 9 + 3 x 8
= 9 + 24
= $33
(b)
Amount that Xandra had at first
= 18 + 6 p
= 18 + 6 x 8
= 18 + 48
= $66
Answer(s): (a) $33; (b) $66
