Owen and Olivia has some money each. If Olivia gives Owen $20, he will have 5 times as much money as her. If Owen gives Olivia $19, he will have the same amount of money as her. How much money does each person have respectively?
- Owen?
- Olivia?
| |
Case 1 |
Case 2 |
| |
Owen |
Olivia |
Owen |
Olivia |
| Before |
5 u - 20 |
1 u + 20 |
3 u + 19 |
3 u - 19 |
| Change |
+ 20 |
- 20 |
- 19 |
+ 19 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Olivia gives Owen some money or Owen gives Olivia some money, the total amount of money remains the same.
Total amount that Owen and Olivia have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Owen and Olivia each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Owen has at first in Case 1 and Case 2 is the same.
5 u - 20 = 3 u + 19
5 u - 3 u = 19 + 20
1 u = 39
Amount that Owen has
= 3 u + 19
= 3 x 39 + 19
= 117 + 19
= $136
(b)
Amount that Olivia has
= 1 u + 20
= 39 + 20
= $59
Answer(s): (a) $136; (b) $59
