Howard and Raeann has some money each. If Raeann gives Howard $12, he will have 5 times as much money as her. If Howard gives Raeann $16, he will have the same amount of money as her. How much money does each person have respectively?
- Howard?
- Raeann?
| |
Case 1 |
Case 2 |
| |
Howard |
Raeann |
Howard |
Raeann |
| Before |
5 u - 12 |
1 u + 12 |
3 u + 16 |
3 u - 16 |
| Change |
+ 12 |
- 12 |
- 16 |
+ 16 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Raeann gives Howard some money or Howard gives Raeann some money, the total amount of money remains the same.
Total amount that Howard and Raeann have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Howard and Raeann each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Howard has at first in Case 1 and Case 2 is the same.
5 u - 12 = 3 u + 16
5 u - 3 u = 16 + 12
1 u = 28
Amount that Howard has
= 3 u + 16
= 3 x 28 + 16
= 84 + 16
= $100
(b)
Amount that Raeann has
= 1 u + 12
= 28 + 12
= $40
Answer(s): (a) $100; (b) $40
