The ratio of Hazel's money to Kathy's money was 1 : 3. After Hazel spent five times as much as Kathy, Hazel and Kathy had $5 and $57 left respectively. Find the amount of money each of the girls have at first.
- Hazel
- Kathy
| |
Make u the same
(1)x3 = (3) |
Hazel
(1) |
Kathy
(2) |
| Before |
3 u |
1 u |
3 u |
| Change |
- 15 p |
- 5 p |
- 1 p |
| After |
15 |
5 |
57 |
(a)
1 u - 5 p = 5
3 u = 5 + 5 p --- (1)
3 u - 1 p = 57
3 u = 57 + 1 p --- (2)
(1)
x3
3 u = 15 + 15 p --- (3)
(3) = (2)
15 + 15 p = 57 + 1 p
15 p - 1 p = 57 - 15
14 p = 42
1 p = 42 ÷ 14 = 3
Amount that Hazel had at first
= 5 + 5 p
= 5 + 5 x 3
= 5 + 15
= $20
(b)
Amount that Kathy had at first
= 15 + 15 p
= 15 + 15 x 3
= 15 + 45
= $60
Answer(s): (a) $20; (b) $60
