The ratio of Vanessa's money to Rachel's money was 1 : 3. After Vanessa spent thrice as much as Rachel, Vanessa and Rachel had $5 and $55 left respectively. Find the amount of money each of the girls have at first.
- Vanessa
- Rachel
| |
Make u the same
(1)x3 = (3) |
Vanessa
(1) |
Rachel
(2) |
| Before |
3 u |
1 u |
3 u |
| Change |
- 9 p |
- 3 p |
- 1 p |
| After |
15 |
5 |
55 |
(a)
1 u - 3 p = 5
3 u = 5 + 3 p --- (1)
3 u - 1 p = 55
3 u = 55 + 1 p --- (2)
(1)
x3
3 u = 15 + 9 p --- (3)
(3) = (2)
15 + 9 p = 55 + 1 p
9 p - 1 p = 55 - 15
8 p = 40
1 p = 40 ÷ 8 = 5
Amount that Vanessa had at first
= 5 + 3 p
= 5 + 3 x 5
= 5 + 15
= $20
(b)
Amount that Rachel had at first
= 15 + 9 p
= 15 + 9 x 5
= 15 + 45
= $60
Answer(s): (a) $20; (b) $60
