The ratio of Hilda's money to Emma's money was 1 : 2. After Hilda spent five times as much as Emma, Hilda and Emma had $6 and $57 left respectively. Find the amount of money each of the girls have at first.
- Hilda
- Emma
| |
Make u the same
(1)x2 = (3) |
Hilda
(1) |
Emma
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 10 p |
- 5 p |
- 1 p |
| After |
12 |
6 |
57 |
(a)
1 u - 5 p = 6
2 u = 6 + 5 p --- (1)
2 u - 1 p = 57
2 u = 57 + 1 p --- (2)
(1)
x2
2 u = 12 + 10 p --- (3)
(3) = (2)
12 + 10 p = 57 + 1 p
10 p - 1 p = 57 - 12
9 p = 45
1 p = 45 ÷ 9 = 5
Amount that Hilda had at first
= 6 + 5 p
= 6 + 5 x 5
= 6 + 25
= $31
(b)
Amount that Emma had at first
= 12 + 10 p
= 12 + 10 x 5
= 12 + 50
= $62
Answer(s): (a) $31; (b) $62
