Peter and Olivia has some money each. If Olivia gives Peter $16, he will have 3 times as much money as her. If Peter gives Olivia $18, he will have the same amount of money as her. How much money does each person have respectively?
- Peter?
- Olivia?
| |
Case 1 |
Case 2 |
| |
Peter |
Olivia |
Peter |
Olivia |
| Before |
3 u - 16 |
1 u + 16 |
2 u + 18 |
2 u - 18 |
| Change |
+ 16 |
- 16 |
- 18 |
+ 18 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Olivia gives Peter some money or Peter gives Olivia some money, the total amount of money remains the same.
Total amount that Peter and Olivia have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Peter and Olivia each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Peter has at first in Case 1 and Case 2 is the same.
3 u - 16 = 2 u + 18
3 u - 2 u = 18 + 16
1 u = 34
Amount that Peter has
= 2 u + 18
= 2 x 34 + 18
= 68 + 18
= $86
(b)
Amount that Olivia has
= 1 u + 16
= 34 + 16
= $50
Answer(s): (a) $86; (b) $50
