The ratio of Barbara's money to Gillian's money was 1 : 4. After Barbara spent thrice as much as Gillian, Barbara and Gillian had $8 and $54 left respectively. Find the amount of money each of the girls have at first.
- Barbara
- Gillian
| |
Make u the same
(1)x4 = (3) |
Barbara
(1) |
Gillian
(2) |
| Before |
4 u |
1 u |
4 u |
| Change |
- 12 p |
- 3 p |
- 1 p |
| After |
32 |
8 |
54 |
(a)
1 u - 3 p = 8
4 u = 8 + 3 p --- (1)
4 u - 1 p = 54
4 u = 54 + 1 p --- (2)
(1)
x4
4 u = 32 + 12 p --- (3)
(3) = (2)
32 + 12 p = 54 + 1 p
12 p - 1 p = 54 - 32
11 p = 22
1 p = 22 ÷ 11 = 2
Amount that Barbara had at first
= 8 + 3 p
= 8 + 3 x 2
= 8 + 6
= $14
(b)
Amount that Gillian had at first
= 32 + 12 p
= 32 + 12 x 2
= 32 + 24
= $56
Answer(s): (a) $14; (b) $56
