The ratio of Gem's money to Jade's money was 1 : 2. After Gem spent five times as much as Jade, Gem and Jade had $4 and $44 left respectively. Find the amount of money each of the girls have at first.
- Gem
- Jade
| |
Make u the same
(1)x2 = (3) |
Gem
(1) |
Jade
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 10 p |
- 5 p |
- 1 p |
| After |
8 |
4 |
44 |
(a)
1 u - 5 p = 4
2 u = 4 + 5 p --- (1)
2 u - 1 p = 44
2 u = 44 + 1 p --- (2)
(1)
x2
2 u = 8 + 10 p --- (3)
(3) = (2)
8 + 10 p = 44 + 1 p
10 p - 1 p = 44 - 8
9 p = 36
1 p = 36 ÷ 9 = 4
Amount that Gem had at first
= 4 + 5 p
= 4 + 5 x 4
= 4 + 20
= $24
(b)
Amount that Jade had at first
= 8 + 10 p
= 8 + 10 x 4
= 8 + 40
= $48
Answer(s): (a) $24; (b) $48
