If Barbara gives Charlie $23, the amount of money she has will be 25% of his. If Charlie gives Barbara $10, he will have the same amount of money as her. How much money did each of them have?
(a) Charlie
(b) Barbara
|
Case 1 |
Case 2 |
|
Charlie |
Barbara |
Charlie |
Barbara |
Before |
4 u - 23 |
1 u + 23 |
2.5 u + 10 |
2.5 u - 10 |
Change |
+ 23 |
- 23 |
- 10 |
+ 10 |
After |
4 u |
1 u |
2.5 u |
2.5 u |
(a)
25% =
25100 =
14 In Case 1, when Barbara gives to Charlie, there is an internal transfer of money from Barbara to Charlie. The total amount that both have remains the same.
In Case 2, when Charlie gives to Barbara, there is an internal transfer of money from Charlie to Barbara. 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 Barbara and Charlie have
= 4 u + 1 u
= 5 u
Amount that Barbara and Charlie each has in the end for Case 2
= 5 u ÷ 2
= 2.5 u
Amount that Charlie has at first is the same in Case 1 and Case 2.
4 u - 23 = 2.5 u + 10
4 u - 2.5 u = 10 + 23
1.5 u = 33
1 u = 33 ÷ 1.5 = 22
Amount that Charlie has
= 4 u - 23
= 4 x 22 - 23
= 88 - 23
= $65
(b)
Amount that Barbara has
= 1 u + 23
= 1 x 22 + 23
= 22 + 23
= $45
Answer(s): (a) $65; (b) $45