Xuan and Kathy have some money. If Xuan spends $1, she will have
35 as much money as Kathy. If Kathy spends $10, Xuan will have
56 as much money as Kathy. How much money does Xuan have?
| |
Case 1 |
Case 2 |
| |
Xuan |
Kathy |
Xuan |
Kathy |
| Before |
3 u + $1 |
5 u |
5 p |
6 p + $10 |
| Change |
- $1 |
|
|
- $10 |
| After |
3 u |
5 u |
5 p |
6 p |
The amount that Xuan has at first in Case 1 and Case 2 is the same.
3 u + 1 = 5 p
3 u = 5 p - 1 --- (1)
The amount that Kathy has at first in Case 1 and Case 2 is the same.
5 u = 6 p + 10 --- (2)
Make u the same.
(1)
x 515 u = 25 p - 5 --- (3)
(2)
x 315 u = 18 p + 30 --- (4)
(3) = (4)
25 p - 5 = 18 p + 30
25 p - 18 p = 5 + 30
7 p = 35
1 p = 35 ÷ 7 = 5
Amount that Xuan has
= 5 p
= 5 x 5
= $25
Answer(s): $25
