The ratio of Gem's money to Opal's money was 1 : 3. After Gem spent five times as much as Opal, Gem and Opal had $5 and $43 left respectively. Find the amount of money each of the girls have at first.
- Gem
- Opal
| |
Make u the same
(1)x3 = (3) |
Gem
(1) |
Opal
(2) |
| Before |
3 u |
1 u |
3 u |
| Change |
- 15 p |
- 5 p |
- 1 p |
| After |
15 |
5 |
43 |
(a)
1 u - 5 p = 5
3 u = 5 + 5 p --- (1)
3 u - 1 p = 43
3 u = 43 + 1 p --- (2)
(1)
x3
3 u = 15 + 15 p --- (3)
(3) = (2)
15 + 15 p = 43 + 1 p
15 p - 1 p = 43 - 15
14 p = 28
1 p = 28 ÷ 14 = 2
Amount that Gem had at first
= 5 + 5 p
= 5 + 5 x 2
= 5 + 10
= $15
(b)
Amount that Opal had at first
= 15 + 15 p
= 15 + 15 x 2
= 15 + 30
= $45
Answer(s): (a) $15; (b) $45
