Gwen and Mary have some money. If Gwen spends $12, she will have
25 as much money as Mary. If Mary spends $18, Gwen will have
67 as much money as Mary. How much money does Gwen have?
| |
Case 1 |
Case 2 |
| |
Gwen |
Mary |
Gwen |
Mary |
| Before |
2 u + $12 |
5 u |
6 p |
7 p + $18 |
| Change |
- $12 |
|
|
- $18 |
| After |
2 u |
5 u |
6 p |
7 p |
The amount that Gwen has at first in Case 1 and Case 2 is the same.
2 u + 12 = 6 p
2 u = 6 p - 12 --- (1)
The amount that Mary has at first in Case 1 and Case 2 is the same.
5 u = 7 p + 18 --- (2)
Make u the same.
(1)
x 510 u = 30 p - 60 --- (3)
(2)
x 210 u = 14 p + 36 --- (4)
(3) = (4)
30 p - 60 = 14 p + 36
30 p - 14 p = 60 + 36
16 p = 96
1 p = 96 ÷ 16 = 6
Amount that Gwen has
= 6 p
= 6 x 6
= $36
Answer(s): $36
