David and Nora has some money each. If Nora gives David $17, he will have 3 times as much money as her. If David gives Nora $15, he will have the same amount of money as her. How much money does each person have respectively?
- David?
- Nora?
| |
Case 1 |
Case 2 |
| |
David |
Nora |
David |
Nora |
| Before |
3 u - 17 |
1 u + 17 |
2 u + 15 |
2 u - 15 |
| Change |
+ 17 |
- 17 |
- 15 |
+ 15 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Nora gives David some money or David gives Nora some money, the total amount of money remains the same.
Total amount that David and Nora have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that David and Nora 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 - 17 = 2 u + 15
3 u - 2 u = 15 + 17
1 u = 32
Amount that David has
= 2 u + 15
= 2 x 32 + 15
= 64 + 15
= $79
(b)
Amount that Nora has
= 1 u + 17
= 32 + 17
= $49
Answer(s): (a) $79; (b) $49
