Gwen and Fiona have some money. If Gwen spends $30, she will have
25 as much money as Fiona. If Fiona spends $5, Gwen will have
67 as much money as Fiona. How much money does Gwen have?
| |
Case 1 |
Case 2 |
| |
Gwen |
Fiona |
Gwen |
Fiona |
| Before |
2 u + $30 |
5 u |
6 p |
7 p + $5 |
| Change |
- $30 |
|
|
- $5 |
| 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 + 30 = 6 p
2 u = 6 p - 30 --- (1)
The amount that Fiona has at first in Case 1 and Case 2 is the same.
5 u = 7 p + 5 --- (2)
Make u the same.
(1)
x 510 u = 30 p - 150 --- (3)
(2)
x 210 u = 14 p + 10 --- (4)
(3) = (4)
30 p - 150 = 14 p + 10
30 p - 14 p = 150 + 10
16 p = 160
1 p = 160 ÷ 16 = 10
Amount that Gwen has
= 6 p
= 6 x 10
= $60
Answer(s): $60
