The ratio of Shiyun's money to Emily's money was 1 : 3. After Shiyun spent five times as much as Emily, Shiyun and Emily had $6 and $46 left respectively. Find the amount of money each of the girls have at first.
- Shiyun
- Emily
| |
Make u the same
(1)x3 = (3) |
Shiyun
(1) |
Emily
(2) |
| Before |
3 u |
1 u |
3 u |
| Change |
- 15 p |
- 5 p |
- 1 p |
| After |
18 |
6 |
46 |
(a)
1 u - 5 p = 6
3 u = 6 + 5 p --- (1)
3 u - 1 p = 46
3 u = 46 + 1 p --- (2)
(1)
x3
3 u = 18 + 15 p --- (3)
(3) = (2)
18 + 15 p = 46 + 1 p
15 p - 1 p = 46 - 18
14 p = 28
1 p = 28 ÷ 14 = 2
Amount that Shiyun had at first
= 6 + 5 p
= 6 + 5 x 2
= 6 + 10
= $16
(b)
Amount that Emily had at first
= 18 + 15 p
= 18 + 15 x 2
= 18 + 30
= $48
Answer(s): (a) $16; (b) $48
