Olivia and Yoko have some money. If Olivia spends $20, she will have
25 as much money as Yoko. If Yoko spends $2, Olivia will have
56 as much money as Yoko. How much money does Yoko have?
| |
Case 1 |
Case 2 |
| |
Olivia |
Yoko |
Olivia |
Yoko |
| Before |
2 u + $20 |
5 u |
5 p |
6 p + $2 |
| Change |
- $20 |
|
|
- $2 |
| After |
2 u |
5 u |
5 p |
6 p |
The amount that Olivia has at first in Case 1 and Case 2 is the same.
2 u + 20 = 5 p
2 u = 5 p - 20 --- (1)
The amount that Yoko has at first in Case 1 and Case 2 is the same.
5 u = 6 p + 2 --- (2)
Make u the same.
(1)
x 510 u = 25 p - 100 --- (3)
(2)
x 210 u = 12 p + 4 --- (4)
(3) = (4)
25 p - 100 = 12 p + 4
25 p - 12 p = 100 + 4
13 p = 104
1 p = 104 ÷ 13 = 8
Amount that Yoko has
= 6 p + 2
= 6 x 8 + 2
= 48 + 2
= $50
Answer(s): $50
