Cathy and Olivia have some money. If Cathy spends $2, she will have
25 as much money as Olivia. If Olivia spends $31, Cathy will have
58 as much money as Olivia. How much money does Cathy have?
| |
Case 1 |
Case 2 |
| |
Cathy |
Olivia |
Cathy |
Olivia |
| Before |
2 u + $2 |
5 u |
5 p |
8 p + $31 |
| Change |
- $2 |
|
|
- $31 |
| After |
2 u |
5 u |
5 p |
8 p |
The amount that Cathy has at first in Case 1 and Case 2 is the same.
2 u + 2 = 5 p
2 u = 5 p - 2 --- (1)
The amount that Olivia has at first in Case 1 and Case 2 is the same.
5 u = 8 p + 31 --- (2)
Make u the same.
(1)
x 510 u = 25 p - 10 --- (3)
(2)
x 210 u = 16 p + 62 --- (4)
(3) = (4)
25 p - 10 = 16 p + 62
25 p - 16 p = 10 + 62
9 p = 72
1 p = 72 ÷ 9 = 8
Amount that Cathy has
= 5 p
= 5 x 8
= $40
Answer(s): $40
