The ratio of Sarah's money to Yen's money was 1 : 2. After Sarah spent thrice as much as Yen, Sarah and Yen had $9 and $38 left respectively. Find the amount of money each of the girls have at first.
- Sarah
- Yen
| |
Make u the same
(1)x2 = (3) |
Sarah
(1) |
Yen
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 6 p |
- 3 p |
- 1 p |
| After |
18 |
9 |
38 |
(a)
1 u - 3 p = 9
2 u = 9 + 3 p --- (1)
2 u - 1 p = 38
2 u = 38 + 1 p --- (2)
(1)
x2
2 u = 18 + 6 p --- (3)
(3) = (2)
18 + 6 p = 38 + 1 p
6 p - 1 p = 38 - 18
5 p = 20
1 p = 20 ÷ 5 = 4
Amount that Sarah had at first
= 9 + 3 p
= 9 + 3 x 4
= 9 + 12
= $21
(b)
Amount that Yen had at first
= 18 + 6 p
= 18 + 6 x 4
= 18 + 24
= $42
Answer(s): (a) $21; (b) $42
