If Kylie gives Reggie $24, the amount of money she has will be 40% of his. If Reggie gives Kylie $42, he will have the same amount of money as her. How much money did each of them have?
(a) Reggie
(b) Kylie
|
Case 1 |
Case 2 |
|
Reggie |
Kylie |
Reggie |
Kylie |
Before |
5 u - 24 |
2 u + 24 |
3.5 u + 42 |
3.5 u - 42 |
Change |
+ 24 |
- 24 |
- 42 |
+ 42 |
After |
5 u |
2 u |
3.5 u |
3.5 u |
(a)
40% =
40100 =
25 In Case 1, when Kylie gives to Reggie, there is an internal transfer of money from Kylie to Reggie. The total amount that both have remains the same.
In Case 2, when Reggie gives to Kylie, there is an internal transfer of money from Reggie 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 Reggie have
= 5 u + 2 u
= 7 u
Amount that Kylie and Reggie each has in the end for Case 2
= 7 u ÷ 2
= 3.5 u
Amount that Reggie has at first is the same in Case 1 and Case 2.
5 u - 24 = 3.5 u + 42
5 u - 3.5 u = 42 + 24
1.5 u = 66
1 u = 66 ÷ 1.5 = 44
Amount that Reggie has
= 5 u - 24
= 5 x 44 - 24
= 220 - 24
= $196
(b)
Amount that Kylie has
= 2 u + 24
= 2 x 44 + 24
= 88 + 24
= $112
Answer(s): (a) $196; (b) $112