The ratio of Gabby's money to Anna's money was 1 : 2. After Gabby spent four times as much as Anna, Gabby and Anna had $8 and $51 left respectively. Find the amount of money each of the girls have at first.
- Gabby
- Anna
| |
Make u the same
(1)x2 = (3) |
Gabby
(1) |
Anna
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 8 p |
- 4 p |
- 1 p |
| After |
16 |
8 |
51 |
(a)
1 u - 4 p = 8
2 u = 8 + 4 p --- (1)
2 u - 1 p = 51
2 u = 51 + 1 p --- (2)
(1)
x2
2 u = 16 + 8 p --- (3)
(3) = (2)
16 + 8 p = 51 + 1 p
8 p - 1 p = 51 - 16
7 p = 35
1 p = 35 ÷ 7 = 5
Amount that Gabby had at first
= 8 + 4 p
= 8 + 4 x 5
= 8 + 20
= $28
(b)
Amount that Anna had at first
= 16 + 8 p
= 16 + 8 x 5
= 16 + 40
= $56
Answer(s): (a) $28; (b) $56
