Oliver and Roshel has some money each. If Roshel gives Oliver $15, he will have 3 times as much money as her. If Oliver gives Roshel $18, he will have the same amount of money as her. How much money does each person have respectively?
- Oliver?
- Roshel?
| |
Case 1 |
Case 2 |
| |
Oliver |
Roshel |
Oliver |
Roshel |
| Before |
3 u - 15 |
1 u + 15 |
2 u + 18 |
2 u - 18 |
| Change |
+ 15 |
- 15 |
- 18 |
+ 18 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Roshel gives Oliver some money or Oliver gives Roshel some money, the total amount of money remains the same.
Total amount that Oliver and Roshel have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Oliver and Roshel each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Oliver has at first in Case 1 and Case 2 is the same.
3 u - 15 = 2 u + 18
3 u - 2 u = 18 + 15
1 u = 33
Amount that Oliver has
= 2 u + 18
= 2 x 33 + 18
= 66 + 18
= $84
(b)
Amount that Roshel has
= 1 u + 15
= 33 + 15
= $48
Answer(s): (a) $84; (b) $48
