The ratio of Shiyun's money to Abi's money was 1 : 2. After Shiyun spent four times as much as Abi, Shiyun and Abi had $7 and $56 left respectively. Find the amount of money each of the girls have at first.
- Shiyun
- Abi
| |
Make u the same
(1)x2 = (3) |
Shiyun
(1) |
Abi
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 8 p |
- 4 p |
- 1 p |
| After |
14 |
7 |
56 |
(a)
1 u - 4 p = 7
2 u = 7 + 4 p --- (1)
2 u - 1 p = 56
2 u = 56 + 1 p --- (2)
(1)
x2
2 u = 14 + 8 p --- (3)
(3) = (2)
14 + 8 p = 56 + 1 p
8 p - 1 p = 56 - 14
7 p = 42
1 p = 42 ÷ 7 = 6
Amount that Shiyun had at first
= 7 + 4 p
= 7 + 4 x 6
= 7 + 24
= $31
(b)
Amount that Abi had at first
= 14 + 8 p
= 14 + 8 x 6
= 14 + 48
= $62
Answer(s): (a) $31; (b) $62
