Cathy and Yoko have some money. If Cathy spends $3, she will have
35 as much money as Yoko. If Yoko spends $16, Cathy will have
56 as much money as Yoko. How much money does Yoko have?
| |
Case 1 |
Case 2 |
| |
Cathy |
Yoko |
Cathy |
Yoko |
| Before |
3 u + $3 |
5 u |
5 p |
6 p + $16 |
| Change |
- $3 |
|
|
- $16 |
| After |
3 u |
5 u |
5 p |
6 p |
The amount that Cathy has at first in Case 1 and Case 2 is the same.
3 u + 3 = 5 p
3 u = 5 p - 3 --- (1)
The amount that Yoko has at first in Case 1 and Case 2 is the same.
5 u = 6 p + 16 --- (2)
Make u the same.
(1)
x 515 u = 25 p - 15 --- (3)
(2)
x 315 u = 18 p + 48 --- (4)
(3) = (4)
25 p - 15 = 18 p + 48
25 p - 18 p = 15 + 48
7 p = 63
1 p = 63 ÷ 7 = 9
Amount that Yoko has
= 6 p + 16
= 6 x 9 + 16
= 54 + 16
= $70
Answer(s): $70
