The ratio of Erika's money to Pamela's money was 1 : 2. After Erika spent four times as much as Pamela, Erika and Pamela had $4 and $43 left respectively. Find the amount of money each of the girls have at first.
- Erika
- Pamela
| |
Make u the same
(1)x2 = (3) |
Erika
(1) |
Pamela
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 8 p |
- 4 p |
- 1 p |
| After |
8 |
4 |
43 |
(a)
1 u - 4 p = 4
2 u = 4 + 4 p --- (1)
2 u - 1 p = 43
2 u = 43 + 1 p --- (2)
(1)
x2
2 u = 8 + 8 p --- (3)
(3) = (2)
8 + 8 p = 43 + 1 p
8 p - 1 p = 43 - 8
7 p = 35
1 p = 35 ÷ 7 = 5
Amount that Erika had at first
= 4 + 4 p
= 4 + 4 x 5
= 4 + 20
= $24
(b)
Amount that Pamela had at first
= 8 + 8 p
= 8 + 8 x 5
= 8 + 40
= $48
Answer(s): (a) $24; (b) $48
