The ratio of Linda's money to Sarah's money was 1 : 2. After Linda spent thrice as much as Sarah, Linda and Sarah had $7 and $54 left respectively. Find the amount of money each of the girls have at first.
- Linda
- Sarah
| |
Make u the same
(1)x2 = (3) |
Linda
(1) |
Sarah
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 6 p |
- 3 p |
- 1 p |
| After |
14 |
7 |
54 |
(a)
1 u - 3 p = 7
2 u = 7 + 3 p --- (1)
2 u - 1 p = 54
2 u = 54 + 1 p --- (2)
(1)
x2
2 u = 14 + 6 p --- (3)
(3) = (2)
14 + 6 p = 54 + 1 p
6 p - 1 p = 54 - 14
5 p = 40
1 p = 40 ÷ 5 = 8
Amount that Linda had at first
= 7 + 3 p
= 7 + 3 x 8
= 7 + 24
= $31
(b)
Amount that Sarah had at first
= 14 + 6 p
= 14 + 6 x 8
= 14 + 48
= $62
Answer(s): (a) $31; (b) $62
