David and Zoe has some money each. If Zoe gives David $20, he will have 3 times as much money as her. If David gives Zoe $17, he will have the same amount of money as her. How much money does each person have respectively?
- David?
- Zoe?
| |
Case 1 |
Case 2 |
| |
David |
Zoe |
David |
Zoe |
| Before |
3 u - 20 |
1 u + 20 |
2 u + 17 |
2 u - 17 |
| Change |
+ 20 |
- 20 |
- 17 |
+ 17 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Zoe gives David some money or David gives Zoe some money, the total amount of money remains the same.
Total amount that David and Zoe have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that David and Zoe each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that David has at first in Case 1 and Case 2 is the same.
3 u - 20 = 2 u + 17
3 u - 2 u = 17 + 20
1 u = 37
Amount that David has
= 2 u + 17
= 2 x 37 + 17
= 74 + 17
= $91
(b)
Amount that Zoe has
= 1 u + 20
= 37 + 20
= $57
Answer(s): (a) $91; (b) $57
