The ratio of Jane's money to Gillian's money was 1 : 4. After Jane spent thrice as much as Gillian, Jane and Gillian had $6 and $57 left respectively. Find the amount of money each of the girls have at first.
- Jane
- Gillian
| |
Make u the same
(1)x4 = (3) |
Jane
(1) |
Gillian
(2) |
| Before |
4 u |
1 u |
4 u |
| Change |
- 12 p |
- 3 p |
- 1 p |
| After |
24 |
6 |
57 |
(a)
1 u - 3 p = 6
4 u = 6 + 3 p --- (1)
4 u - 1 p = 57
4 u = 57 + 1 p --- (2)
(1)
x4
4 u = 24 + 12 p --- (3)
(3) = (2)
24 + 12 p = 57 + 1 p
12 p - 1 p = 57 - 24
11 p = 33
1 p = 33 ÷ 11 = 3
Amount that Jane had at first
= 6 + 3 p
= 6 + 3 x 3
= 6 + 9
= $15
(b)
Amount that Gillian had at first
= 24 + 12 p
= 24 + 12 x 3
= 24 + 36
= $60
Answer(s): (a) $15; (b) $60
