The ratio of Gem's money to Ivory's money was 1 : 2. After Gem spent thrice as much as Ivory, Gem and Ivory had $4 and $58 left respectively. Find the amount of money each of the girls have at first.
- Gem
- Ivory
| |
Make u the same
(1)x2 = (3) |
Gem
(1) |
Ivory
(2) |
| Before |
2 u |
1 u |
2 u |
| Change |
- 6 p |
- 3 p |
- 1 p |
| After |
8 |
4 |
58 |
(a)
1 u - 3 p = 4
2 u = 4 + 3 p --- (1)
2 u - 1 p = 58
2 u = 58 + 1 p --- (2)
(1)
x2
2 u = 8 + 6 p --- (3)
(3) = (2)
8 + 6 p = 58 + 1 p
6 p - 1 p = 58 - 8
5 p = 50
1 p = 50 ÷ 5 = 10
Amount that Gem had at first
= 4 + 3 p
= 4 + 3 x 10
= 4 + 30
= $34
(b)
Amount that Ivory had at first
= 8 + 6 p
= 8 + 6 x 10
= 8 + 60
= $68
Answer(s): (a) $34; (b) $68
