The ratio of Diana's money to Gabby's money was 1 : 5. After Diana spent thrice as much as Gabby, Diana and Gabby had $5 and $53 left respectively. Find the amount of money each of the girls have at first.
- Diana
- Gabby
| |
Make u the same
(1)x5 = (3) |
Diana
(1) |
Gabby
(2) |
| Before |
5 u |
1 u |
5 u |
| Change |
- 15 p |
- 3 p |
- 1 p |
| After |
25 |
5 |
53 |
(a)
1 u - 3 p = 5
5 u = 5 + 3 p --- (1)
5 u - 1 p = 53
5 u = 53 + 1 p --- (2)
(1)
x5
5 u = 25 + 15 p --- (3)
(3) = (2)
25 + 15 p = 53 + 1 p
15 p - 1 p = 53 - 25
14 p = 28
1 p = 28 ÷ 14 = 2
Amount that Diana had at first
= 5 + 3 p
= 5 + 3 x 2
= 5 + 6
= $11
(b)
Amount that Gabby had at first
= 25 + 15 p
= 25 + 15 x 2
= 25 + 30
= $55
Answer(s): (a) $11; (b) $55
