The ratio of Emma's money to Fanny's money was 1 : 2. After Emma spent four times as much as Fanny, Emma and Fanny had $6 and $54 left respectively. Find the amount of money each of the girls have at first.
- Emma
- Fanny
| |
Make u the same
(1)x2 = (3) |
Emma
(1) |
Fanny
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 8 p |
- 4 p |
- 1 p |
| After |
12 |
6 |
54 |
(a)
1 u - 4 p = 6
2 u = 6 + 4 p --- (1)
2 u - 1 p = 54
2 u = 54 + 1 p --- (2)
(1)
x2
2 u = 12 + 8 p --- (3)
(3) = (2)
12 + 8 p = 54 + 1 p
8 p - 1 p = 54 - 12
7 p = 42
1 p = 42 ÷ 7 = 6
Amount that Emma had at first
= 6 + 4 p
= 6 + 4 x 6
= 6 + 24
= $30
(b)
Amount that Fanny had at first
= 12 + 8 p
= 12 + 8 x 6
= 12 + 48
= $60
Answer(s): (a) $30; (b) $60
