The ratio of Erika's money to Min's money was 1 : 2. After Erika spent thrice as much as Min, Erika and Min had $8 and $36 left respectively. Find the amount of money each of the girls have at first.
- Erika
- Min
| |
Make u the same
(1)x2 = (3) |
Erika
(1) |
Min
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 6 p |
- 3 p |
- 1 p |
| After |
16 |
8 |
36 |
(a)
1 u - 3 p = 8
2 u = 8 + 3 p --- (1)
2 u - 1 p = 36
2 u = 36 + 1 p --- (2)
(1)
x2
2 u = 16 + 6 p --- (3)
(3) = (2)
16 + 6 p = 36 + 1 p
6 p - 1 p = 36 - 16
5 p = 20
1 p = 20 ÷ 5 = 4
Amount that Erika had at first
= 8 + 3 p
= 8 + 3 x 4
= 8 + 12
= $20
(b)
Amount that Min had at first
= 16 + 6 p
= 16 + 6 x 4
= 16 + 24
= $40
Answer(s): (a) $20; (b) $40
