The ratio of Erika's money to Fanny's money was 1 : 3. After Erika spent five times as much as Fanny, Erika and Fanny had $7 and $49 left respectively. Find the amount of money each of the girls have at first.
- Erika
- Fanny
| |
Make u the same
(1)x3 = (3) |
Erika
(1) |
Fanny
(2) |
| Before |
3 u |
1 u |
3 u |
| Change |
- 15 p |
- 5 p |
- 1 p |
| After |
21 |
7 |
49 |
(a)
1 u - 5 p = 7
3 u = 7 + 5 p --- (1)
3 u - 1 p = 49
3 u = 49 + 1 p --- (2)
(1)
x3
3 u = 21 + 15 p --- (3)
(3) = (2)
21 + 15 p = 49 + 1 p
15 p - 1 p = 49 - 21
14 p = 28
1 p = 28 ÷ 14 = 2
Amount that Erika had at first
= 7 + 5 p
= 7 + 5 x 2
= 7 + 10
= $17
(b)
Amount that Fanny had at first
= 21 + 15 p
= 21 + 15 x 2
= 21 + 30
= $51
Answer(s): (a) $17; (b) $51
