Pierre and Roshel has some money each. If Roshel gives Pierre $16, he will have 3 times as much money as her. If Pierre gives Roshel $14, he will have the same amount of money as her. How much money does each person have respectively?
- Pierre?
- Roshel?
|
Case 1 |
Case 2 |
|
Pierre |
Roshel |
Pierre |
Roshel |
Before |
3 u - 16 |
1 u + 16 |
2 u + 14 |
2 u - 14 |
Change |
+ 16 |
- 16 |
- 14 |
+ 14 |
After |
3 u |
1 u |
2 u |
2 u |
(a)
If Roshel gives Pierre some money or Pierre gives Roshel some money, the total amount of money remains the same.
Total amount that Pierre and Roshel have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Pierre and Roshel each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Pierre has at first in Case 1 and Case 2 is the same.
3 u - 16 = 2 u + 14
3 u - 2 u = 14 + 16
1 u = 30
Amount that Pierre has
= 2 u + 14
= 2 x 30 + 14
= 60 + 14
= $74
(b)
Amount that Roshel has
= 1 u + 16
= 30 + 16
= $46
Answer(s): (a) $74; (b) $46