The ratio of Roshel's money to Yen's money was 1 : 4. After Roshel spent thrice as much as Yen, Roshel and Yen had $4 and $49 left respectively. Find the amount of money each of the girls have at first.
- Roshel
- Yen
| |
Make u the same
(1)x4 = (3) |
Roshel
(1) |
Yen
(2) |
| Before |
4 u |
1 u |
4 u |
| Change |
- 12 p |
- 3 p |
- 1 p |
| After |
16 |
4 |
49 |
(a)
1 u - 3 p = 4
4 u = 4 + 3 p --- (1)
4 u - 1 p = 49
4 u = 49 + 1 p --- (2)
(1)
x4
4 u = 16 + 12 p --- (3)
(3) = (2)
16 + 12 p = 49 + 1 p
12 p - 1 p = 49 - 16
11 p = 33
1 p = 33 ÷ 11 = 3
Amount that Roshel had at first
= 4 + 3 p
= 4 + 3 x 3
= 4 + 9
= $13
(b)
Amount that Yen had at first
= 16 + 12 p
= 16 + 12 x 3
= 16 + 36
= $52
Answer(s): (a) $13; (b) $52
