If Risa gives Perry $24, the amount of money she has will be 25% of his. If Perry gives Risa $9, he will have the same amount of money as her. How much money did each of them have?
(a) Perry
(b) Risa
|
Case 1 |
Case 2 |
|
Perry |
Risa |
Perry |
Risa |
Before |
4 u - 24 |
1 u + 24 |
2.5 u + 9 |
2.5 u - 9 |
Change |
+ 24 |
- 24 |
- 9 |
+ 9 |
After |
4 u |
1 u |
2.5 u |
2.5 u |
(a)
25% =
25100 =
14 In Case 1, when Risa gives to Perry, there is an internal transfer of money from Risa to Perry. The total amount that both have remains the same.
In Case 2, when Perry gives to Risa, there is an internal transfer of money from Perry to Risa. 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 Risa and Perry have
= 4 u + 1 u
= 5 u
Amount that Risa and Perry each has in the end for Case 2
= 5 u ÷ 2
= 2.5 u
Amount that Perry has at first is the same in Case 1 and Case 2.
4 u - 24 = 2.5 u + 9
4 u - 2.5 u = 9 + 24
1.5 u = 33
1 u = 33 ÷ 1.5 = 22
Amount that Perry has
= 4 u - 24
= 4 x 22 - 24
= 88 - 24
= $64
(b)
Amount that Risa has
= 1 u + 24
= 1 x 22 + 24
= 22 + 24
= $46
Answer(s): (a) $64; (b) $46