The ratio of Rachel's money to Diana's money was 1 : 2. After Rachel spent thrice as much as Diana, Rachel and Diana had $4 and $53 left respectively. Find the amount of money each of the girls have at first.
- Rachel
- Diana
| |
Make u the same
(1)x2 = (3) |
Rachel
(1) |
Diana
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 6 p |
- 3 p |
- 1 p |
| After |
8 |
4 |
53 |
(a)
1 u - 3 p = 4
2 u = 4 + 3 p --- (1)
2 u - 1 p = 53
2 u = 53 + 1 p --- (2)
(1)
x2
2 u = 8 + 6 p --- (3)
(3) = (2)
8 + 6 p = 53 + 1 p
6 p - 1 p = 53 - 8
5 p = 45
1 p = 45 ÷ 5 = 9
Amount that Rachel had at first
= 4 + 3 p
= 4 + 3 x 9
= 4 + 27
= $31
(b)
Amount that Diana had at first
= 8 + 6 p
= 8 + 6 x 9
= 8 + 54
= $62
Answer(s): (a) $31; (b) $62
