Brandon and Hazel has some money each. If Hazel gives Brandon $14, he will have 3 times as much money as her. If Brandon gives Hazel $15, he will have the same amount of money as her. How much money does each person have respectively?
- Brandon?
- Hazel?
| |
Case 1 |
Case 2 |
| |
Brandon |
Hazel |
Brandon |
Hazel |
| Before |
3 u - 14 |
1 u + 14 |
2 u + 15 |
2 u - 15 |
| Change |
+ 14 |
- 14 |
- 15 |
+ 15 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Hazel gives Brandon some money or Brandon gives Hazel some money, the total amount of money remains the same.
Total amount that Brandon and Hazel have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Brandon and Hazel each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Brandon has at first in Case 1 and Case 2 is the same.
3 u - 14 = 2 u + 15
3 u - 2 u = 15 + 14
1 u = 29
Amount that Brandon has
= 2 u + 15
= 2 x 29 + 15
= 58 + 15
= $73
(b)
Amount that Hazel has
= 1 u + 14
= 29 + 14
= $43
Answer(s): (a) $73; (b) $43
