If Kathy gives Cody $36, the amount of money she has will be 40% of his. If Cody gives Kathy $15, he will have the same amount of money as her. How much money did each of them have?
(a) Cody
(b) Kathy
|
Case 1 |
Case 2 |
|
Cody |
Kathy |
Cody |
Kathy |
Before |
5 u - 36 |
2 u + 36 |
3.5 u + 15 |
3.5 u - 15 |
Change |
+ 36 |
- 36 |
- 15 |
+ 15 |
After |
5 u |
2 u |
3.5 u |
3.5 u |
(a)
40% =
40100 =
25 In Case 1, when Kathy gives to Cody, there is an internal transfer of money from Kathy to Cody. The total amount that both have remains the same.
In Case 2, when Cody gives to Kathy, there is an internal transfer of money from Cody to Kathy. 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 Kathy and Cody have
= 5 u + 2 u
= 7 u
Amount that Kathy and Cody each has in the end for Case 2
= 7 u ÷ 2
= 3.5 u
Amount that Cody has at first is the same in Case 1 and Case 2.
5 u - 36 = 3.5 u + 15
5 u - 3.5 u = 15 + 36
1.5 u = 51
1 u = 51 ÷ 1.5 = 34
Amount that Cody has
= 5 u - 36
= 5 x 34 - 36
= 170 - 36
= $134
(b)
Amount that Kathy has
= 2 u + 36
= 2 x 34 + 36
= 68 + 36
= $104
Answer(s): (a) $134; (b) $104