If Fiona gives Michael $20, the amount of money she has will be 25% of his. If Michael gives Fiona $52, he will have the same amount of money as her. How much money did each of them have?
(a) Michael
(b) Fiona
|
Case 1 |
Case 2 |
|
Michael |
Fiona |
Michael |
Fiona |
Before |
4 u - 20 |
1 u + 20 |
2.5 u + 52 |
2.5 u - 52 |
Change |
+ 20 |
- 20 |
- 52 |
+ 52 |
After |
4 u |
1 u |
2.5 u |
2.5 u |
(a)
25% =
25100 =
14 In Case 1, when Fiona gives to Michael, there is an internal transfer of money from Fiona to Michael. The total amount that both have remains the same.
In Case 2, when Michael gives to Fiona, there is an internal transfer of money from Michael to Fiona. 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 Fiona and Michael have
= 4 u + 1 u
= 5 u
Amount that Fiona and Michael each has in the end for Case 2
= 5 u ÷ 2
= 2.5 u
Amount that Michael has at first is the same in Case 1 and Case 2.
4 u - 20 = 2.5 u + 52
4 u - 2.5 u = 52 + 20
1.5 u = 72
1 u = 72 ÷ 1.5 = 48
Amount that Michael has
= 4 u - 20
= 4 x 48 - 20
= 192 - 20
= $172
(b)
Amount that Fiona has
= 1 u + 20
= 1 x 48 + 20
= 48 + 20
= $68
Answer(s): (a) $172; (b) $68