If Victoria gives Justin $30, the amount of money she has will be 25% of his. If Justin gives Victoria $33, he will have the same amount of money as her. How much money did each of them have?
(a) Justin
(b) Victoria
|
Case 1 |
Case 2 |
|
Justin |
Victoria |
Justin |
Victoria |
Before |
4 u - 30 |
1 u + 30 |
2.5 u + 33 |
2.5 u - 33 |
Change |
+ 30 |
- 30 |
- 33 |
+ 33 |
After |
4 u |
1 u |
2.5 u |
2.5 u |
(a)
25% =
25100 =
14 In Case 1, when Victoria gives to Justin, there is an internal transfer of money from Victoria to Justin. The total amount that both have remains the same.
In Case 2, when Justin gives to Victoria, there is an internal transfer of money from Justin to Victoria. 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 Victoria and Justin have
= 4 u + 1 u
= 5 u
Amount that Victoria and Justin each has in the end for Case 2
= 5 u ÷ 2
= 2.5 u
Amount that Justin has at first is the same in Case 1 and Case 2.
4 u - 30 = 2.5 u + 33
4 u - 2.5 u = 33 + 30
1.5 u = 63
1 u = 63 ÷ 1.5 = 42
Amount that Justin has
= 4 u - 30
= 4 x 42 - 30
= 168 - 30
= $138
(b)
Amount that Victoria has
= 1 u + 30
= 1 x 42 + 30
= 42 + 30
= $72
Answer(s): (a) $138; (b) $72