Dana and Fanny have some money. If Dana spends $31, she will have
25 as much money as Fanny. If Fanny spends $7, Dana will have
56 as much money as Fanny. How much money does Dana have?
| |
Case 1 |
Case 2 |
| |
Dana |
Fanny |
Dana |
Fanny |
| Before |
2 u + $31 |
5 u |
5 p |
6 p + $7 |
| Change |
- $31 |
|
|
- $7 |
| After |
2 u |
5 u |
5 p |
6 p |
The amount that Dana has at first in Case 1 and Case 2 is the same.
2 u + 31 = 5 p
2 u = 5 p - 31 --- (1)
The amount that Fanny has at first in Case 1 and Case 2 is the same.
5 u = 6 p + 7 --- (2)
Make u the same.
(1)
x 510 u = 25 p - 155 --- (3)
(2)
x 210 u = 12 p + 14 --- (4)
(3) = (4)
25 p - 155 = 12 p + 14
25 p - 12 p = 155 + 14
13 p = 169
1 p = 169 ÷ 13 = 13
Amount that Dana has
= 5 p
= 5 x 13
= $65
Answer(s): $65
