If Kylie gives Flynn $40, the amount of money she has will be 30% of his. If Flynn gives Kylie $37, he will have the same amount of money as her. How much money did each of them have?
(a) Flynn
(b) Kylie
|
Case 1 |
Case 2 |
|
Flynn |
Kylie |
Flynn |
Kylie |
Before |
10 u - 40 |
3 u + 40 |
6.5 u + 37 |
6.5 u - 37 |
Change |
+ 40 |
- 40 |
- 37 |
+ 37 |
After |
10 u |
3 u |
6.5 u |
6.5 u |
(a)
30% =
30100 =
310 In Case 1, when Kylie gives to Flynn, there is an internal transfer of money from Kylie to Flynn. The total amount that both have remains the same.
In Case 2, when Flynn gives to Kylie, there is an internal transfer of money from Flynn to Kylie. 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 Kylie and Flynn have
= 10 u + 3 u
= 13 u
Amount that Kylie and Flynn each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u
Amount that Flynn has at first is the same in Case 1 and Case 2.
10 u - 40 = 6.5 u + 37
10 u - 6.5 u = 37 + 40
3.5 u = 77
1 u = 77 ÷ 3.5 = 22
Amount that Flynn has
= 10 u - 40
= 10 x 22 - 40
= 220 - 40
= $180
(b)
Amount that Kylie has
= 3 u + 40
= 3 x 22 + 40
= 66 + 40
= $106
Answer(s): (a) $180; (b) $106