If Gem gives Jack $33, the amount of money she has will be 25% of his. If Jack gives Gem $36, he will have the same amount of money as her. How much money did each of them have?
(a) Jack
(b) Gem
|
Case 1 |
Case 2 |
|
Jack |
Gem |
Jack |
Gem |
Before |
4 u - 33 |
1 u + 33 |
2.5 u + 36 |
2.5 u - 36 |
Change |
+ 33 |
- 33 |
- 36 |
+ 36 |
After |
4 u |
1 u |
2.5 u |
2.5 u |
(a)
25% =
25100 =
14 In Case 1, when Gem gives to Jack, there is an internal transfer of money from Gem to Jack. The total amount that both have remains the same.
In Case 2, when Jack gives to Gem, there is an internal transfer of money from Jack to Gem. 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 Gem and Jack have
= 4 u + 1 u
= 5 u
Amount that Gem and Jack each has in the end for Case 2
= 5 u ÷ 2
= 2.5 u
Amount that Jack has at first is the same in Case 1 and Case 2.
4 u - 33 = 2.5 u + 36
4 u - 2.5 u = 36 + 33
1.5 u = 69
1 u = 69 ÷ 1.5 = 46
Amount that Jack has
= 4 u - 33
= 4 x 46 - 33
= 184 - 33
= $151
(b)
Amount that Gem has
= 1 u + 33
= 1 x 46 + 33
= 46 + 33
= $79
Answer(s): (a) $151; (b) $79