Paul and Roshel has some money each. If Roshel gives Paul $14, he will have 3 times as much money as her. If Paul gives Roshel $16, he will have the same amount of money as her. How much money does each person have respectively?
- Paul?
- Roshel?
| |
Case 1 |
Case 2 |
| |
Paul |
Roshel |
Paul |
Roshel |
| Before |
3 u - 14 |
1 u + 14 |
2 u + 16 |
2 u - 16 |
| Change |
+ 14 |
- 14 |
- 16 |
+ 16 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Roshel gives Paul some money or Paul gives Roshel some money, the total amount of money remains the same.
Total amount that Paul and Roshel have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Paul and Roshel each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Paul has at first in Case 1 and Case 2 is the same.
3 u - 14 = 2 u + 16
3 u - 2 u = 16 + 14
1 u = 30
Amount that Paul has
= 2 u + 16
= 2 x 30 + 16
= 60 + 16
= $76
(b)
Amount that Roshel has
= 1 u + 14
= 30 + 14
= $44
Answer(s): (a) $76; (b) $44
