The ratio of Zara's money to Cathy's money was 1 : 2. After Zara spent thrice as much as Cathy, Zara and Cathy had $6 and $57 left respectively. Find the amount of money each of the girls have at first.
- Zara
- Cathy
| |
Make u the same
(1)x2 = (3) |
Zara
(1) |
Cathy
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 6 p |
- 3 p |
- 1 p |
| After |
12 |
6 |
57 |
(a)
1 u - 3 p = 6
2 u = 6 + 3 p --- (1)
2 u - 1 p = 57
2 u = 57 + 1 p --- (2)
(1)
x2
2 u = 12 + 6 p --- (3)
(3) = (2)
12 + 6 p = 57 + 1 p
6 p - 1 p = 57 - 12
5 p = 45
1 p = 45 ÷ 5 = 9
Amount that Zara had at first
= 6 + 3 p
= 6 + 3 x 9
= 6 + 27
= $33
(b)
Amount that Cathy had at first
= 12 + 6 p
= 12 + 6 x 9
= 12 + 54
= $66
Answer(s): (a) $33; (b) $66
