If Olivia gives Fred $32, the amount of money she has will be 40% of his. If Fred gives Olivia $13, he will have the same amount of money as her. How much money did each of them have?
(a) Fred
(b) Olivia
|
Case 1 |
Case 2 |
|
Fred |
Olivia |
Fred |
Olivia |
Before |
5 u - 32 |
2 u + 32 |
3.5 u + 13 |
3.5 u - 13 |
Change |
+ 32 |
- 32 |
- 13 |
+ 13 |
After |
5 u |
2 u |
3.5 u |
3.5 u |
(a)
40% =
40100 =
25 In Case 1, when Olivia gives to Fred, there is an internal transfer of money from Olivia to Fred. The total amount that both have remains the same.
In Case 2, when Fred gives to Olivia, there is an internal transfer of money from Fred to Olivia. 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 Olivia and Fred have
= 5 u + 2 u
= 7 u
Amount that Olivia and Fred each has in the end for Case 2
= 7 u ÷ 2
= 3.5 u
Amount that Fred has at first is the same in Case 1 and Case 2.
5 u - 32 = 3.5 u + 13
5 u - 3.5 u = 13 + 32
1.5 u = 45
1 u = 45 ÷ 1.5 = 30
Amount that Fred has
= 5 u - 32
= 5 x 30 - 32
= 150 - 32
= $118
(b)
Amount that Olivia has
= 2 u + 32
= 2 x 30 + 32
= 60 + 32
= $92
Answer(s): (a) $118; (b) $92