The ratio of Opal's money to Yen's money was 1 : 4. After Opal spent five times as much as Yen, Opal and Yen had $5 and $58 left respectively. Find the amount of money each of the girls have at first.
- Opal
- Yen
| |
Make u the same
(1)x4 = (3) |
Opal
(1) |
Yen
(2) |
| Before |
4 u |
1 u |
4 u |
| Change |
- 20 p |
- 5 p |
- 1 p |
| After |
20 |
5 |
58 |
(a)
1 u - 5 p = 5
4 u = 5 + 5 p --- (1)
4 u - 1 p = 58
4 u = 58 + 1 p --- (2)
(1)
x4
4 u = 20 + 20 p --- (3)
(3) = (2)
20 + 20 p = 58 + 1 p
20 p - 1 p = 58 - 20
19 p = 38
1 p = 38 ÷ 19 = 2
Amount that Opal had at first
= 5 + 5 p
= 5 + 5 x 2
= 5 + 10
= $15
(b)
Amount that Yen had at first
= 20 + 20 p
= 20 + 20 x 2
= 20 + 40
= $60
Answer(s): (a) $15; (b) $60
