Vincent and Kimberly has some money each. If Kimberly gives Vincent $16, he will have 5 times as much money as her. If Vincent gives Kimberly $14, he will have the same amount of money as her. How much money does each person have respectively?
- Vincent?
- Kimberly?
|
Case 1 |
Case 2 |
|
Vincent |
Kimberly |
Vincent |
Kimberly |
Before |
5 u - 16 |
1 u + 16 |
3 u + 14 |
3 u - 14 |
Change |
+ 16 |
- 16 |
- 14 |
+ 14 |
After |
5 u |
1 u |
3 u |
3 u |
(a)
If Kimberly gives Vincent some money or Vincent gives Kimberly some money, the total amount of money remains the same.
Total amount that Vincent and Kimberly have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Vincent and Kimberly each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Vincent has at first in Case 1 and Case 2 is the same.
5 u - 16 = 3 u + 14
5 u - 3 u = 14 + 16
1 u = 30
Amount that Vincent has
= 3 u + 14
= 3 x 30 + 14
= 90 + 14
= $104
(b)
Amount that Kimberly has
= 1 u + 16
= 30 + 16
= $46
Answer(s): (a) $104; (b) $46