Oliver and Kimberly has some money each. If Kimberly gives Oliver $19, he will have 5 times as much money as her. If Oliver gives Kimberly $14, he will have the same amount of money as her. How much money does each person have respectively?
- Oliver?
- Kimberly?
|
Case 1 |
Case 2 |
|
Oliver |
Kimberly |
Oliver |
Kimberly |
Before |
5 u - 19 |
1 u + 19 |
3 u + 14 |
3 u - 14 |
Change |
+ 19 |
- 19 |
- 14 |
+ 14 |
After |
5 u |
1 u |
3 u |
3 u |
(a)
If Kimberly gives Oliver some money or Oliver gives Kimberly some money, the total amount of money remains the same.
Total amount that Oliver and Kimberly have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Oliver and Kimberly each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Oliver has at first in Case 1 and Case 2 is the same.
5 u - 19 = 3 u + 14
5 u - 3 u = 14 + 19
1 u = 33
Amount that Oliver has
= 3 u + 14
= 3 x 33 + 14
= 99 + 14
= $113
(b)
Amount that Kimberly has
= 1 u + 19
= 33 + 19
= $52
Answer(s): (a) $113; (b) $52