David and Hazel has some money each. If Hazel gives David $18, he will have 3 times as much money as her. If David gives Hazel $19, he will have the same amount of money as her. How much money does each person have respectively?
- David?
- Hazel?
| |
Case 1 |
Case 2 |
| |
David |
Hazel |
David |
Hazel |
| Before |
3 u - 18 |
1 u + 18 |
2 u + 19 |
2 u - 19 |
| Change |
+ 18 |
- 18 |
- 19 |
+ 19 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Hazel gives David some money or David gives Hazel some money, the total amount of money remains the same.
Total amount that David and Hazel have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that David and Hazel 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 - 18 = 2 u + 19
3 u - 2 u = 19 + 18
1 u = 37
Amount that David has
= 2 u + 19
= 2 x 37 + 19
= 74 + 19
= $93
(b)
Amount that Hazel has
= 1 u + 18
= 37 + 18
= $55
Answer(s): (a) $93; (b) $55
