Jenson and Kimberly has some money each. If Kimberly gives Jenson $16, he will have 7 times as much money as her. If Jenson gives Kimberly $10, he will have the same amount of money as her. How much money does each person have respectively?
- Jenson?
- Kimberly?
|
Case 1 |
Case 2 |
|
Jenson |
Kimberly |
Jenson |
Kimberly |
Before |
7 u - 16 |
1 u + 16 |
4 u + 10 |
4 u - 10 |
Change |
+ 16 |
- 16 |
- 10 |
+ 10 |
After |
7 u |
1 u |
4 u |
4 u |
(a)
If Kimberly gives Jenson some money or Jenson gives Kimberly some money, the total amount of money remains the same.
Total amount that Jenson and Kimberly have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Jenson and Kimberly each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Jenson has at first in Case 1 and Case 2 is the same.
7 u - 16 = 4 u + 10
7 u - 4 u = 10 + 16
1 u = 26
Amount that Jenson has
= 4 u + 10
= 4 x 26 + 10
= 104 + 10
= $114
(b)
Amount that Kimberly has
= 1 u + 16
= 26 + 16
= $42
Answer(s): (a) $114; (b) $42