Cathy and Joelle have some money. If Cathy spends $5, she will have
35 as much money as Joelle. If Joelle spends $9, Cathy will have
57 as much money as Joelle. How much money does Cathy have?
| |
Case 1 |
Case 2 |
| |
Cathy |
Joelle |
Cathy |
Joelle |
| Before |
3 u + $5 |
5 u |
5 p |
7 p + $9 |
| Change |
- $5 |
|
|
- $9 |
| After |
3 u |
5 u |
5 p |
7 p |
The amount that Cathy has at first in Case 1 and Case 2 is the same.
3 u + 5 = 5 p
3 u = 5 p - 5 --- (1)
The amount that Joelle has at first in Case 1 and Case 2 is the same.
5 u = 7 p + 9 --- (2)
Make u the same.
(1)
x 515 u = 25 p - 25 --- (3)
(2)
x 315 u = 21 p + 27 --- (4)
(3) = (4)
25 p - 25 = 21 p + 27
25 p - 21 p = 25 + 27
4 p = 52
1 p = 52 ÷ 4 = 13
Amount that Cathy has
= 5 p
= 5 x 13
= $65
Answer(s): $65
