The ratio of Hilda's money to Marion's money was 1 : 2. After Hilda spent five times as much as Marion, Hilda and Marion had $5 and $46 left respectively. Find the amount of money each of the girls have at first.
- Hilda
- Marion
| |
Make u the same
(1)x2 = (3) |
Hilda
(1) |
Marion
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 10 p |
- 5 p |
- 1 p |
| After |
10 |
5 |
46 |
(a)
1 u - 5 p = 5
2 u = 5 + 5 p --- (1)
2 u - 1 p = 46
2 u = 46 + 1 p --- (2)
(1)
x2
2 u = 10 + 10 p --- (3)
(3) = (2)
10 + 10 p = 46 + 1 p
10 p - 1 p = 46 - 10
9 p = 36
1 p = 36 ÷ 9 = 4
Amount that Hilda had at first
= 5 + 5 p
= 5 + 5 x 4
= 5 + 20
= $25
(b)
Amount that Marion had at first
= 10 + 10 p
= 10 + 10 x 4
= 10 + 40
= $50
Answer(s): (a) $25; (b) $50
