The ratio of Barbara's money to Shannon's money was 1 : 2. After Barbara spent thrice as much as Shannon, Barbara and Shannon had $7 and $44 left respectively. Find the amount of money each of the girls have at first.
- Barbara
- Shannon
| |
Make u the same
(1)x2 = (3) |
Barbara
(1) |
Shannon
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 6 p |
- 3 p |
- 1 p |
| After |
14 |
7 |
44 |
(a)
1 u - 3 p = 7
2 u = 7 + 3 p --- (1)
2 u - 1 p = 44
2 u = 44 + 1 p --- (2)
(1)
x2
2 u = 14 + 6 p --- (3)
(3) = (2)
14 + 6 p = 44 + 1 p
6 p - 1 p = 44 - 14
5 p = 30
1 p = 30 ÷ 5 = 6
Amount that Barbara had at first
= 7 + 3 p
= 7 + 3 x 6
= 7 + 18
= $25
(b)
Amount that Shannon had at first
= 14 + 6 p
= 14 + 6 x 6
= 14 + 36
= $50
Answer(s): (a) $25; (b) $50
