The ratio of Linda's money to Gem's money was 1 : 2. After Linda spent four times as much as Gem, Linda and Gem had $4 and $36 left respectively. Find the amount of money each of the girls have at first.
- Linda
- Gem
| |
Make u the same
(1)x2 = (3) |
Linda
(1) |
Gem
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 8 p |
- 4 p |
- 1 p |
| After |
8 |
4 |
36 |
(a)
1 u - 4 p = 4
2 u = 4 + 4 p --- (1)
2 u - 1 p = 36
2 u = 36 + 1 p --- (2)
(1)
x2
2 u = 8 + 8 p --- (3)
(3) = (2)
8 + 8 p = 36 + 1 p
8 p - 1 p = 36 - 8
7 p = 28
1 p = 28 ÷ 7 = 4
Amount that Linda had at first
= 4 + 4 p
= 4 + 4 x 4
= 4 + 16
= $20
(b)
Amount that Gem had at first
= 8 + 8 p
= 8 + 8 x 4
= 8 + 32
= $40
Answer(s): (a) $20; (b) $40
