Vaidev and Usha has some money each. If Usha gives Vaidev $12, he will have 3 times as much money as her. If Vaidev gives Usha $19, he will have the same amount of money as her. How much money does each person have respectively?
- Vaidev?
- Usha?
| |
Case 1 |
Case 2 |
| |
Vaidev |
Usha |
Vaidev |
Usha |
| Before |
3 u - 12 |
1 u + 12 |
2 u + 19 |
2 u - 19 |
| Change |
+ 12 |
- 12 |
- 19 |
+ 19 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Usha gives Vaidev some money or Vaidev gives Usha some money, the total amount of money remains the same.
Total amount that Vaidev and Usha have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Vaidev and Usha each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Vaidev has at first in Case 1 and Case 2 is the same.
3 u - 12 = 2 u + 19
3 u - 2 u = 19 + 12
1 u = 31
Amount that Vaidev has
= 2 u + 19
= 2 x 31 + 19
= 62 + 19
= $81
(b)
Amount that Usha has
= 1 u + 12
= 31 + 12
= $43
Answer(s): (a) $81; (b) $43
