Jenson and Olivia has some money each. If Olivia gives Jenson $10, he will have 5 times as much money as her. If Jenson gives Olivia $13, he will have the same amount of money as her. How much money does each person have respectively?
- Jenson?
- Olivia?
|
Case 1 |
Case 2 |
|
Jenson |
Olivia |
Jenson |
Olivia |
Before |
5 u - 10 |
1 u + 10 |
3 u + 13 |
3 u - 13 |
Change |
+ 10 |
- 10 |
- 13 |
+ 13 |
After |
5 u |
1 u |
3 u |
3 u |
(a)
If Olivia gives Jenson some money or Jenson gives Olivia some money, the total amount of money remains the same.
Total amount that Jenson and Olivia have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Jenson and Olivia each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Jenson has at first in Case 1 and Case 2 is the same.
5 u - 10 = 3 u + 13
5 u - 3 u = 13 + 10
1 u = 23
Amount that Jenson has
= 3 u + 13
= 3 x 23 + 13
= 69 + 13
= $82
(b)
Amount that Olivia has
= 1 u + 10
= 23 + 10
= $33
Answer(s): (a) $82; (b) $33