Valen and Hazel has some money each. If Hazel gives Valen $16, he will have 5 times as much money as her. If Valen gives Hazel $13, he will have the same amount of money as her. How much money does each person have respectively?
- Valen?
- Hazel?
| |
Case 1 |
Case 2 |
| |
Valen |
Hazel |
Valen |
Hazel |
| Before |
5 u - 16 |
1 u + 16 |
3 u + 13 |
3 u - 13 |
| Change |
+ 16 |
- 16 |
- 13 |
+ 13 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Hazel gives Valen some money or Valen gives Hazel some money, the total amount of money remains the same.
Total amount that Valen and Hazel have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Valen and Hazel each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Valen has at first in Case 1 and Case 2 is the same.
5 u - 16 = 3 u + 13
5 u - 3 u = 13 + 16
1 u = 29
Amount that Valen has
= 3 u + 13
= 3 x 29 + 13
= 87 + 13
= $100
(b)
Amount that Hazel has
= 1 u + 16
= 29 + 16
= $45
Answer(s): (a) $100; (b) $45
