Oscar and Hazel has some money each. If Hazel gives Oscar $16, he will have 3 times as much money as her. If Oscar gives Hazel $20, he will have the same amount of money as her. How much money does each person have respectively?
- Oscar?
- Hazel?
| |
Case 1 |
Case 2 |
| |
Oscar |
Hazel |
Oscar |
Hazel |
| Before |
3 u - 16 |
1 u + 16 |
2 u + 20 |
2 u - 20 |
| Change |
+ 16 |
- 16 |
- 20 |
+ 20 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Hazel gives Oscar some money or Oscar gives Hazel some money, the total amount of money remains the same.
Total amount that Oscar and Hazel have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Oscar and Hazel each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Oscar has at first in Case 1 and Case 2 is the same.
3 u - 16 = 2 u + 20
3 u - 2 u = 20 + 16
1 u = 36
Amount that Oscar has
= 2 u + 20
= 2 x 36 + 20
= 72 + 20
= $92
(b)
Amount that Hazel has
= 1 u + 16
= 36 + 16
= $52
Answer(s): (a) $92; (b) $52
