The ratio of Barbara's money to Erika's money was 1 : 2. After Barbara spent thrice as much as Erika, Barbara and Erika had $6 and $52 left respectively. Find the amount of money each of the girls have at first.
- Barbara
- Erika
| |
Make u the same
(1)x2 = (3) |
Barbara
(1) |
Erika
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 6 p |
- 3 p |
- 1 p |
| After |
12 |
6 |
52 |
(a)
1 u - 3 p = 6
2 u = 6 + 3 p --- (1)
2 u - 1 p = 52
2 u = 52 + 1 p --- (2)
(1)
x2
2 u = 12 + 6 p --- (3)
(3) = (2)
12 + 6 p = 52 + 1 p
6 p - 1 p = 52 - 12
5 p = 40
1 p = 40 ÷ 5 = 8
Amount that Barbara had at first
= 6 + 3 p
= 6 + 3 x 8
= 6 + 24
= $30
(b)
Amount that Erika had at first
= 12 + 6 p
= 12 + 6 x 8
= 12 + 48
= $60
Answer(s): (a) $30; (b) $60
