David and Dana has some money each. If Dana gives David $20, he will have 5 times as much money as her. If David gives Dana $15, he will have the same amount of money as her. How much money does each person have respectively?
- David?
- Dana?
|
Case 1 |
Case 2 |
|
David |
Dana |
David |
Dana |
Before |
5 u - 20 |
1 u + 20 |
3 u + 15 |
3 u - 15 |
Change |
+ 20 |
- 20 |
- 15 |
+ 15 |
After |
5 u |
1 u |
3 u |
3 u |
(a)
If Dana gives David some money or David gives Dana some money, the total amount of money remains the same.
Total amount that David and Dana have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that David and Dana each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that David has at first in Case 1 and Case 2 is the same.
5 u - 20 = 3 u + 15
5 u - 3 u = 15 + 20
1 u = 35
Amount that David has
= 3 u + 15
= 3 x 35 + 15
= 105 + 15
= $120
(b)
Amount that Dana has
= 1 u + 20
= 35 + 20
= $55
Answer(s): (a) $120; (b) $55