If Kylie gives Sean $30, the amount of money she has will be 30% of his. If Sean gives Kylie $110, he will have the same amount of money as her. How much money did each of them have?
(a) Sean
(b) Kylie
|
Case 1 |
Case 2 |
|
Sean |
Kylie |
Sean |
Kylie |
Before |
10 u - 30 |
3 u + 30 |
6.5 u + 110 |
6.5 u - 110 |
Change |
+ 30 |
- 30 |
- 110 |
+ 110 |
After |
10 u |
3 u |
6.5 u |
6.5 u |
(a)
30% =
30100 =
310 In Case 1, when Kylie gives to Sean, there is an internal transfer of money from Kylie to Sean. The total amount that both have remains the same.
In Case 2, when Sean gives to Kylie, there is an internal transfer of money from Sean 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 Sean have
= 10 u + 3 u
= 13 u
Amount that Kylie and Sean each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u
Amount that Sean has at first is the same in Case 1 and Case 2.
10 u - 30 = 6.5 u + 110
10 u - 6.5 u = 110 + 30
3.5 u = 140
1 u = 140 ÷ 3.5 = 40
Amount that Sean has
= 10 u - 30
= 10 x 40 - 30
= 400 - 30
= $370
(b)
Amount that Kylie has
= 3 u + 30
= 3 x 40 + 30
= 120 + 30
= $150
Answer(s): (a) $370; (b) $150