Opal and Cathy have some money. If Opal spends $39, she will have
25 as much money as Cathy. If Cathy spends $7, Opal will have
78 as much money as Cathy. How much money does Cathy have?
| |
Case 1 |
Case 2 |
| |
Opal |
Cathy |
Opal |
Cathy |
| Before |
2 u + $39 |
5 u |
7 p |
8 p + $7 |
| Change |
- $39 |
|
|
- $7 |
| After |
2 u |
5 u |
7 p |
8 p |
The amount that Opal has at first in Case 1 and Case 2 is the same.
2 u + 39 = 7 p
2 u = 7 p - 39 --- (1)
The amount that Cathy has at first in Case 1 and Case 2 is the same.
5 u = 8 p + 7 --- (2)
Make u the same.
(1)
x 510 u = 35 p - 195 --- (3)
(2)
x 210 u = 16 p + 14 --- (4)
(3) = (4)
35 p - 195 = 16 p + 14
35 p - 16 p = 195 + 14
19 p = 209
1 p = 209 ÷ 19 = 11
Amount that Cathy has
= 8 p + 7
= 8 x 11 + 7
= 88 + 7
= $95
Answer(s): $95
