Brandon and Gabby has some money each. If Gabby gives Brandon $20, he will have 5 times as much money as her. If Brandon gives Gabby $14, he will have the same amount of money as her. How much money does each person have respectively?
- Brandon?
- Gabby?
| |
Case 1 |
Case 2 |
| |
Brandon |
Gabby |
Brandon |
Gabby |
| Before |
5 u - 20 |
1 u + 20 |
3 u + 14 |
3 u - 14 |
| Change |
+ 20 |
- 20 |
- 14 |
+ 14 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Gabby gives Brandon some money or Brandon gives Gabby some money, the total amount of money remains the same.
Total amount that Brandon and Gabby have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Brandon and Gabby each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Brandon has at first in Case 1 and Case 2 is the same.
5 u - 20 = 3 u + 14
5 u - 3 u = 14 + 20
1 u = 34
Amount that Brandon has
= 3 u + 14
= 3 x 34 + 14
= 102 + 14
= $116
(b)
Amount that Gabby has
= 1 u + 20
= 34 + 20
= $54
Answer(s): (a) $116; (b) $54
