If Vanessa gives Oliver $31, the amount of money she has will be 25% of his. If Oliver gives Vanessa $26, he will have the same amount of money as her. How much money did each of them have?
(a) Oliver
(b) Vanessa
|
Case 1 |
Case 2 |
|
Oliver |
Vanessa |
Oliver |
Vanessa |
Before |
4 u - 31 |
1 u + 31 |
2.5 u + 26 |
2.5 u - 26 |
Change |
+ 31 |
- 31 |
- 26 |
+ 26 |
After |
4 u |
1 u |
2.5 u |
2.5 u |
(a)
25% =
25100 =
14 In Case 1, when Vanessa gives to Oliver, there is an internal transfer of money from Vanessa to Oliver. The total amount that both have remains the same.
In Case 2, when Oliver gives to Vanessa, there is an internal transfer of money from Oliver to Vanessa. The total amount that both have remains the same.
The total amount that both have in Case 1 and Case 2 are the same.
Total amount that Vanessa and Oliver have
= 4 u + 1 u
= 5 u
Amount that Vanessa and Oliver each has in the end for Case 2
= 5 u ÷ 2
= 2.5 u
Amount that Oliver has at first is the same in Case 1 and Case 2.
4 u - 31 = 2.5 u + 26
4 u - 2.5 u = 26 + 31
1.5 u = 57
1 u = 57 ÷ 1.5 = 38
Amount that Oliver has
= 4 u - 31
= 4 x 38 - 31
= 152 - 31
= $121
(b)
Amount that Vanessa has
= 1 u + 31
= 1 x 38 + 31
= 38 + 31
= $69
Answer(s): (a) $121; (b) $69