The ratio of Shannon's money to Linda's money was 1 : 2. After Shannon spent five times as much as Linda, Shannon and Linda had $9 and $45 left respectively. Find the amount of money each of the girls have at first.
- Shannon
- Linda
| |
Make u the same
(1)x2 = (3) |
Shannon
(1) |
Linda
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 10 p |
- 5 p |
- 1 p |
| After |
18 |
9 |
45 |
(a)
1 u - 5 p = 9
2 u = 9 + 5 p --- (1)
2 u - 1 p = 45
2 u = 45 + 1 p --- (2)
(1)
x2
2 u = 18 + 10 p --- (3)
(3) = (2)
18 + 10 p = 45 + 1 p
10 p - 1 p = 45 - 18
9 p = 27
1 p = 27 ÷ 9 = 3
Amount that Shannon had at first
= 9 + 5 p
= 9 + 5 x 3
= 9 + 15
= $24
(b)
Amount that Linda had at first
= 18 + 10 p
= 18 + 10 x 3
= 18 + 30
= $48
Answer(s): (a) $24; (b) $48
