The ratio of Zoe's money to Kathy's money was 1 : 4. After Zoe spent thrice as much as Kathy, Zoe and Kathy had $5 and $42 left respectively. Find the amount of money each of the girls have at first.
- Zoe
- Kathy
| |
Make u the same
(1)x4 = (3) |
Zoe
(1) |
Kathy
(2) |
| Before |
4 u |
1 u |
4 u |
| Change |
- 12 p |
- 3 p |
- 1 p |
| After |
20 |
5 |
42 |
(a)
1 u - 3 p = 5
4 u = 5 + 3 p --- (1)
4 u - 1 p = 42
4 u = 42 + 1 p --- (2)
(1)
x4
4 u = 20 + 12 p --- (3)
(3) = (2)
20 + 12 p = 42 + 1 p
12 p - 1 p = 42 - 20
11 p = 22
1 p = 22 ÷ 11 = 2
Amount that Zoe had at first
= 5 + 3 p
= 5 + 3 x 2
= 5 + 6
= $11
(b)
Amount that Kathy had at first
= 20 + 12 p
= 20 + 12 x 2
= 20 + 24
= $44
Answer(s): (a) $11; (b) $44
