The ratio of Raeann's money to Jean's money was 1 : 3. After Raeann spent four times as much as Jean, Raeann and Jean had $5 and $37 left respectively. Find the amount of money each of the girls have at first.
- Raeann
- Jean
| |
Make u the same
(1)x3 = (3) |
Raeann
(1) |
Jean
(2) |
| Before |
3 u |
1 u |
3 u |
| Change |
- 12 p |
- 4 p |
- 1 p |
| After |
15 |
5 |
37 |
(a)
1 u - 4 p = 5
3 u = 5 + 4 p --- (1)
3 u - 1 p = 37
3 u = 37 + 1 p --- (2)
(1)
x3
3 u = 15 + 12 p --- (3)
(3) = (2)
15 + 12 p = 37 + 1 p
12 p - 1 p = 37 - 15
11 p = 22
1 p = 22 ÷ 11 = 2
Amount that Raeann had at first
= 5 + 4 p
= 5 + 4 x 2
= 5 + 8
= $13
(b)
Amount that Jean had at first
= 15 + 12 p
= 15 + 12 x 2
= 15 + 24
= $39
Answer(s): (a) $13; (b) $39
