The ratio of Zoe's money to Dana's money was 1 : 2. After Zoe spent five times as much as Dana, Zoe and Dana had $6 and $48 left respectively. Find the amount of money each of the girls have at first.
- Zoe
- Dana
| |
Make u the same
(1)x2 = (3) |
Zoe
(1) |
Dana
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 10 p |
- 5 p |
- 1 p |
| After |
12 |
6 |
48 |
(a)
1 u - 5 p = 6
2 u = 6 + 5 p --- (1)
2 u - 1 p = 48
2 u = 48 + 1 p --- (2)
(1)
x2
2 u = 12 + 10 p --- (3)
(3) = (2)
12 + 10 p = 48 + 1 p
10 p - 1 p = 48 - 12
9 p = 36
1 p = 36 ÷ 9 = 4
Amount that Zoe had at first
= 6 + 5 p
= 6 + 5 x 4
= 6 + 20
= $26
(b)
Amount that Dana had at first
= 12 + 10 p
= 12 + 10 x 4
= 12 + 40
= $52
Answer(s): (a) $26; (b) $52
