The ratio of Shiyun's money to Gwen's money was 1 : 2. After Shiyun spent four times as much as Gwen, Shiyun and Gwen had $5 and $52 left respectively. Find the amount of money each of the girls have at first.
- Shiyun
- Gwen
| |
Make u the same
(1)x2 = (3) |
Shiyun
(1) |
Gwen
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 8 p |
- 4 p |
- 1 p |
| After |
10 |
5 |
52 |
(a)
1 u - 4 p = 5
2 u = 5 + 4 p --- (1)
2 u - 1 p = 52
2 u = 52 + 1 p --- (2)
(1)
x2
2 u = 10 + 8 p --- (3)
(3) = (2)
10 + 8 p = 52 + 1 p
8 p - 1 p = 52 - 10
7 p = 42
1 p = 42 ÷ 7 = 6
Amount that Shiyun had at first
= 5 + 4 p
= 5 + 4 x 6
= 5 + 24
= $29
(b)
Amount that Gwen had at first
= 10 + 8 p
= 10 + 8 x 6
= 10 + 48
= $58
Answer(s): (a) $29; (b) $58
