The ratio of Yoko's money to Yen's money was 1 : 4. After Yoko spent four times as much as Yen, Yoko and Yen had $6 and $54 left respectively. Find the amount of money each of the girls have at first.
- Yoko
- Yen
| |
Make u the same
(1)x4 = (3) |
Yoko
(1) |
Yen
(2) |
| Before |
4 u |
1 u |
4 u |
| Change |
- 16 p |
- 4 p |
- 1 p |
| After |
24 |
6 |
54 |
(a)
1 u - 4 p = 6
4 u = 6 + 4 p --- (1)
4 u - 1 p = 54
4 u = 54 + 1 p --- (2)
(1)
x4
4 u = 24 + 16 p --- (3)
(3) = (2)
24 + 16 p = 54 + 1 p
16 p - 1 p = 54 - 24
15 p = 30
1 p = 30 ÷ 15 = 2
Amount that Yoko had at first
= 6 + 4 p
= 6 + 4 x 2
= 6 + 8
= $14
(b)
Amount that Yen had at first
= 24 + 16 p
= 24 + 16 x 2
= 24 + 32
= $56
Answer(s): (a) $14; (b) $56
