Fred and Dana has some money each. If Dana gives Fred $15, he will have 7 times as much money as her. If Fred gives Dana $18, he will have the same amount of money as her. How much money does each person have respectively?
- Fred?
- Dana?
|
Case 1 |
Case 2 |
|
Fred |
Dana |
Fred |
Dana |
Before |
7 u - 15 |
1 u + 15 |
4 u + 18 |
4 u - 18 |
Change |
+ 15 |
- 15 |
- 18 |
+ 18 |
After |
7 u |
1 u |
4 u |
4 u |
(a)
If Dana gives Fred some money or Fred gives Dana some money, the total amount of money remains the same.
Total amount that Fred and Dana have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Fred and Dana each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Fred has at first in Case 1 and Case 2 is the same.
7 u - 15 = 4 u + 18
7 u - 4 u = 18 + 15
1 u = 33
Amount that Fred has
= 4 u + 18
= 4 x 33 + 18
= 132 + 18
= $150
(b)
Amount that Dana has
= 1 u + 15
= 33 + 15
= $48
Answer(s): (a) $150; (b) $48