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