Oliver and Shannon has some money each. If Shannon gives Oliver $20, he will have 3 times as much money as her. If Oliver gives Shannon $14, he will have the same amount of money as her. How much money does each person have respectively?
- Oliver?
- Shannon?
|
Case 1 |
Case 2 |
|
Oliver |
Shannon |
Oliver |
Shannon |
Before |
3 u - 20 |
1 u + 20 |
2 u + 14 |
2 u - 14 |
Change |
+ 20 |
- 20 |
- 14 |
+ 14 |
After |
3 u |
1 u |
2 u |
2 u |
(a)
If Shannon gives Oliver some money or Oliver gives Shannon some money, the total amount of money remains the same.
Total amount that Oliver and Shannon have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Oliver and Shannon each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Oliver has at first in Case 1 and Case 2 is the same.
3 u - 20 = 2 u + 14
3 u - 2 u = 14 + 20
1 u = 34
Amount that Oliver has
= 2 u + 14
= 2 x 34 + 14
= 68 + 14
= $82
(b)
Amount that Shannon has
= 1 u + 20
= 34 + 20
= $54
Answer(s): (a) $82; (b) $54