David and Raeann has some money each. If Raeann gives David $14, he will have 3 times as much money as her. If David gives Raeann $13, he will have the same amount of money as her. How much money does each person have respectively?
- David?
- Raeann?
| |
Case 1 |
Case 2 |
| |
David |
Raeann |
David |
Raeann |
| Before |
3 u - 14 |
1 u + 14 |
2 u + 13 |
2 u - 13 |
| Change |
+ 14 |
- 14 |
- 13 |
+ 13 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Raeann gives David some money or David gives Raeann some money, the total amount of money remains the same.
Total amount that David and Raeann have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that David and Raeann 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 - 14 = 2 u + 13
3 u - 2 u = 13 + 14
1 u = 27
Amount that David has
= 2 u + 13
= 2 x 27 + 13
= 54 + 13
= $67
(b)
Amount that Raeann has
= 1 u + 14
= 27 + 14
= $41
Answer(s): (a) $67; (b) $41
