The ratio of Hilda's money to Gabby's money was 1 : 3. After Hilda spent four times as much as Gabby, Hilda and Gabby had $8 and $57 left respectively. Find the amount of money each of the girls have at first.
- Hilda
- Gabby
| |
Make u the same
(1)x3 = (3) |
Hilda
(1) |
Gabby
(2) |
| Before |
3 u |
1 u |
3 u |
| Change |
- 12 p |
- 4 p |
- 1 p |
| After |
24 |
8 |
57 |
(a)
1 u - 4 p = 8
3 u = 8 + 4 p --- (1)
3 u - 1 p = 57
3 u = 57 + 1 p --- (2)
(1)
x3
3 u = 24 + 12 p --- (3)
(3) = (2)
24 + 12 p = 57 + 1 p
12 p - 1 p = 57 - 24
11 p = 33
1 p = 33 ÷ 11 = 3
Amount that Hilda had at first
= 8 + 4 p
= 8 + 4 x 3
= 8 + 12
= $20
(b)
Amount that Gabby had at first
= 24 + 12 p
= 24 + 12 x 3
= 24 + 36
= $60
Answer(s): (a) $20; (b) $60
