The ratio of Zoe's money to Erika's money was 1 : 2. After Zoe spent thrice as much as Erika, Zoe and Erika had $5 and $50 left respectively. Find the amount of money each of the girls have at first.
- Zoe
- Erika
| |
Make u the same
(1)x2 = (3) |
Zoe
(1) |
Erika
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 6 p |
- 3 p |
- 1 p |
| After |
10 |
5 |
50 |
(a)
1 u - 3 p = 5
2 u = 5 + 3 p --- (1)
2 u - 1 p = 50
2 u = 50 + 1 p --- (2)
(1)
x2
2 u = 10 + 6 p --- (3)
(3) = (2)
10 + 6 p = 50 + 1 p
6 p - 1 p = 50 - 10
5 p = 40
1 p = 40 ÷ 5 = 8
Amount that Zoe had at first
= 5 + 3 p
= 5 + 3 x 8
= 5 + 24
= $29
(b)
Amount that Erika had at first
= 10 + 6 p
= 10 + 6 x 8
= 10 + 48
= $58
Answer(s): (a) $29; (b) $58
