Reggie and Usha has some money each. If Usha gives Reggie $14, he will have 7 times as much money as her. If Reggie gives Usha $12, he will have the same amount of money as her. How much money does each person have respectively?
- Reggie?
- Usha?
|
Case 1 |
Case 2 |
|
Reggie |
Usha |
Reggie |
Usha |
Before |
7 u - 14 |
1 u + 14 |
4 u + 12 |
4 u - 12 |
Change |
+ 14 |
- 14 |
- 12 |
+ 12 |
After |
7 u |
1 u |
4 u |
4 u |
(a)
If Usha gives Reggie some money or Reggie gives Usha some money, the total amount of money remains the same.
Total amount that Reggie and Usha have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Reggie and Usha each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Reggie has at first in Case 1 and Case 2 is the same.
7 u - 14 = 4 u + 12
7 u - 4 u = 12 + 14
1 u = 26
Amount that Reggie has
= 4 u + 12
= 4 x 26 + 12
= 104 + 12
= $116
(b)
Amount that Usha has
= 1 u + 14
= 26 + 14
= $40
Answer(s): (a) $116; (b) $40