The ratio of Rachel's money to Dana's money was 1 : 2. After Rachel spent four times as much as Dana, Rachel and Dana had $9 and $39 left respectively. Find the amount of money each of the girls have at first.
- Rachel
- Dana
| |
Make u the same
(1)x2 = (3) |
Rachel
(1) |
Dana
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 8 p |
- 4 p |
- 1 p |
| After |
18 |
9 |
39 |
(a)
1 u - 4 p = 9
2 u = 9 + 4 p --- (1)
2 u - 1 p = 39
2 u = 39 + 1 p --- (2)
(1)
x2
2 u = 18 + 8 p --- (3)
(3) = (2)
18 + 8 p = 39 + 1 p
8 p - 1 p = 39 - 18
7 p = 21
1 p = 21 ÷ 7 = 3
Amount that Rachel had at first
= 9 + 4 p
= 9 + 4 x 3
= 9 + 12
= $21
(b)
Amount that Dana had at first
= 18 + 8 p
= 18 + 8 x 3
= 18 + 24
= $42
Answer(s): (a) $21; (b) $42
