The ratio of Lucy's money to Shiyun's money was 1 : 2. After Lucy spent four times as much as Shiyun, Lucy and Shiyun had $8 and $58 left respectively. Find the amount of money each of the girls have at first.
- Lucy
- Shiyun
| |
Make u the same
(1)x2 = (3) |
Lucy
(1) |
Shiyun
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 8 p |
- 4 p |
- 1 p |
| After |
16 |
8 |
58 |
(a)
1 u - 4 p = 8
2 u = 8 + 4 p --- (1)
2 u - 1 p = 58
2 u = 58 + 1 p --- (2)
(1)
x2
2 u = 16 + 8 p --- (3)
(3) = (2)
16 + 8 p = 58 + 1 p
8 p - 1 p = 58 - 16
7 p = 42
1 p = 42 ÷ 7 = 6
Amount that Lucy had at first
= 8 + 4 p
= 8 + 4 x 6
= 8 + 24
= $32
(b)
Amount that Shiyun had at first
= 16 + 8 p
= 16 + 8 x 6
= 16 + 48
= $64
Answer(s): (a) $32; (b) $64
