If Jane gives Perry $39, the amount of money she has will be 30% of his. If Perry gives Jane $73, he will have the same amount of money as her. How much money did each of them have?
(a) Perry
(b) Jane
|
Case 1 |
Case 2 |
|
Perry |
Jane |
Perry |
Jane |
Before |
10 u - 39 |
3 u + 39 |
6.5 u + 73 |
6.5 u - 73 |
Change |
+ 39 |
- 39 |
- 73 |
+ 73 |
After |
10 u |
3 u |
6.5 u |
6.5 u |
(a)
30% =
30100 =
310 In Case 1, when Jane gives to Perry, there is an internal transfer of money from Jane to Perry. The total amount that both have remains the same.
In Case 2, when Perry gives to Jane, there is an internal transfer of money from Perry to Jane. 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 Jane and Perry have
= 10 u + 3 u
= 13 u
Amount that Jane and Perry each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u
Amount that Perry has at first is the same in Case 1 and Case 2.
10 u - 39 = 6.5 u + 73
10 u - 6.5 u = 73 + 39
3.5 u = 112
1 u = 112 ÷ 3.5 = 32
Amount that Perry has
= 10 u - 39
= 10 x 32 - 39
= 320 - 39
= $281
(b)
Amount that Jane has
= 3 u + 39
= 3 x 32 + 39
= 96 + 39
= $135
Answer(s): (a) $281; (b) $135