Brandon and Usha has some money each. If Usha gives Brandon $17, he will have 5 times as much money as her. If Brandon gives Usha $18, he will have the same amount of money as her. How much money does each person have respectively?
- Brandon?
- Usha?
| |
Case 1 |
Case 2 |
| |
Brandon |
Usha |
Brandon |
Usha |
| Before |
5 u - 17 |
1 u + 17 |
3 u + 18 |
3 u - 18 |
| Change |
+ 17 |
- 17 |
- 18 |
+ 18 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Usha gives Brandon some money or Brandon gives Usha some money, the total amount of money remains the same.
Total amount that Brandon and Usha have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Brandon and Usha 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 - 17 = 3 u + 18
5 u - 3 u = 18 + 17
1 u = 35
Amount that Brandon has
= 3 u + 18
= 3 x 35 + 18
= 105 + 18
= $123
(b)
Amount that Usha has
= 1 u + 17
= 35 + 17
= $52
Answer(s): (a) $123; (b) $52
