The ratio of Nora's money to Fanny's money was 1 : 2. After Nora spent four times as much as Fanny, Nora and Fanny had $6 and $40 left respectively. Find the amount of money each of the girls have at first.
- Nora
- Fanny
| |
Make u the same
(1)x2 = (3) |
Nora
(1) |
Fanny
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 8 p |
- 4 p |
- 1 p |
| After |
12 |
6 |
40 |
(a)
1 u - 4 p = 6
2 u = 6 + 4 p --- (1)
2 u - 1 p = 40
2 u = 40 + 1 p --- (2)
(1)
x2
2 u = 12 + 8 p --- (3)
(3) = (2)
12 + 8 p = 40 + 1 p
8 p - 1 p = 40 - 12
7 p = 28
1 p = 28 ÷ 7 = 4
Amount that Nora had at first
= 6 + 4 p
= 6 + 4 x 4
= 6 + 16
= $22
(b)
Amount that Fanny had at first
= 12 + 8 p
= 12 + 8 x 4
= 12 + 32
= $44
Answer(s): (a) $22; (b) $44
