Marion and Gwen have some money. If Marion spends $40, she will have
25 as much money as Gwen. If Gwen spends $4, Marion will have
67 as much money as Gwen. How much money does Gwen have?
| |
Case 1 |
Case 2 |
| |
Marion |
Gwen |
Marion |
Gwen |
| Before |
2 u + $40 |
5 u |
6 p |
7 p + $4 |
| Change |
- $40 |
|
|
- $4 |
| After |
2 u |
5 u |
6 p |
7 p |
The amount that Marion has at first in Case 1 and Case 2 is the same.
2 u + 40 = 6 p
2 u = 6 p - 40 --- (1)
The amount that Gwen has at first in Case 1 and Case 2 is the same.
5 u = 7 p + 4 --- (2)
Make u the same.
(1)
x 510 u = 30 p - 200 --- (3)
(2)
x 210 u = 14 p + 8 --- (4)
(3) = (4)
30 p - 200 = 14 p + 8
30 p - 14 p = 200 + 8
16 p = 208
1 p = 208 ÷ 16 = 13
Amount that Gwen has
= 7 p + 4
= 7 x 13 + 4
= 91 + 4
= $95
Answer(s): $95
