The ratio of Wendy's money to Jane's money was 1 : 2. After Wendy spent thrice as much as Jane, Wendy and Jane had $6 and $42 left respectively. Find the amount of money each of the girls have at first.
- Wendy
- Jane
| |
Make u the same
(1)x2 = (3) |
Wendy
(1) |
Jane
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 6 p |
- 3 p |
- 1 p |
| After |
12 |
6 |
42 |
(a)
1 u - 3 p = 6
2 u = 6 + 3 p --- (1)
2 u - 1 p = 42
2 u = 42 + 1 p --- (2)
(1)
x2
2 u = 12 + 6 p --- (3)
(3) = (2)
12 + 6 p = 42 + 1 p
6 p - 1 p = 42 - 12
5 p = 30
1 p = 30 ÷ 5 = 6
Amount that Wendy had at first
= 6 + 3 p
= 6 + 3 x 6
= 6 + 18
= $24
(b)
Amount that Jane had at first
= 12 + 6 p
= 12 + 6 x 6
= 12 + 36
= $48
Answer(s): (a) $24; (b) $48
