The ratio of Wendy's money to Jean's money was 1 : 2. After Wendy spent five times as much as Jean, Wendy and Jean had $4 and $35 left respectively. Find the amount of money each of the girls have at first.
- Wendy
- Jean
| |
Make u the same
(1)x2 = (3) |
Wendy
(1) |
Jean
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 10 p |
- 5 p |
- 1 p |
| After |
8 |
4 |
35 |
(a)
1 u - 5 p = 4
2 u = 4 + 5 p --- (1)
2 u - 1 p = 35
2 u = 35 + 1 p --- (2)
(1)
x2
2 u = 8 + 10 p --- (3)
(3) = (2)
8 + 10 p = 35 + 1 p
10 p - 1 p = 35 - 8
9 p = 27
1 p = 27 ÷ 9 = 3
Amount that Wendy had at first
= 4 + 5 p
= 4 + 5 x 3
= 4 + 15
= $19
(b)
Amount that Jean had at first
= 8 + 10 p
= 8 + 10 x 3
= 8 + 30
= $38
Answer(s): (a) $19; (b) $38
