The ratio of Gem's money to Anna's money was 1 : 4. After Gem spent four times as much as Anna, Gem and Anna had $5 and $50 left respectively. Find the amount of money each of the girls have at first.
- Gem
- Anna
| |
Make u the same
(1)x4 = (3) |
Gem
(1) |
Anna
(2) |
| Before |
4 u |
1 u |
4 u |
| Change |
- 16 p |
- 4 p |
- 1 p |
| After |
20 |
5 |
50 |
(a)
1 u - 4 p = 5
4 u = 5 + 4 p --- (1)
4 u - 1 p = 50
4 u = 50 + 1 p --- (2)
(1)
x4
4 u = 20 + 16 p --- (3)
(3) = (2)
20 + 16 p = 50 + 1 p
16 p - 1 p = 50 - 20
15 p = 30
1 p = 30 ÷ 15 = 2
Amount that Gem had at first
= 5 + 4 p
= 5 + 4 x 2
= 5 + 8
= $13
(b)
Amount that Anna had at first
= 20 + 16 p
= 20 + 16 x 2
= 20 + 32
= $52
Answer(s): (a) $13; (b) $52
