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