The ratio of Diana's money to Marion's money was 1 : 2. After Diana spent four times as much as Marion, Diana and Marion had $5 and $38 left respectively. Find the amount of money each of the girls have at first.
- Diana
- Marion
| |
Make u the same
(1)x2 = (3) |
Diana
(1) |
Marion
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 8 p |
- 4 p |
- 1 p |
| After |
10 |
5 |
38 |
(a)
1 u - 4 p = 5
2 u = 5 + 4 p --- (1)
2 u - 1 p = 38
2 u = 38 + 1 p --- (2)
(1)
x2
2 u = 10 + 8 p --- (3)
(3) = (2)
10 + 8 p = 38 + 1 p
8 p - 1 p = 38 - 10
7 p = 28
1 p = 28 ÷ 7 = 4
Amount that Diana had at first
= 5 + 4 p
= 5 + 4 x 4
= 5 + 16
= $21
(b)
Amount that Marion had at first
= 10 + 8 p
= 10 + 8 x 4
= 10 + 32
= $42
Answer(s): (a) $21; (b) $42
