If Julie gives Charlie $19, the amount of money she has will be 10% of his. If Charlie gives Julie $107, he will have the same amount of money as her. How much money did each of them have?
(a) Charlie
(b) Julie
|
Case 1 |
Case 2 |
|
Charlie |
Julie |
Charlie |
Julie |
Before |
10 u - 19 |
1 u + 19 |
5.5 u + 107 |
5.5 u - 107 |
Change |
+ 19 |
- 19 |
- 107 |
+ 107 |
After |
10 u |
1 u |
5.5 u |
5.5 u |
(a)
10% =
10100 =
110 In Case 1, when Julie gives to Charlie, there is an internal transfer of money from Julie to Charlie. The total amount that both have remains the same.
In Case 2, when Charlie gives to Julie, there is an internal transfer of money from Charlie to Julie. 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 Julie and Charlie have
= 10 u + 1 u
= 11 u
Amount that Julie and Charlie each has in the end for Case 2
= 11 u ÷ 2
= 5.5 u
Amount that Charlie has at first is the same in Case 1 and Case 2.
10 u - 19 = 5.5 u + 107
10 u - 5.5 u = 107 + 19
4.5 u = 126
1 u = 126 ÷ 4.5 = 28
Amount that Charlie has
= 10 u - 19
= 10 x 28 - 19
= 280 - 19
= $261
(b)
Amount that Julie has
= 1 u + 19
= 1 x 28 + 19
= 28 + 19
= $47
Answer(s): (a) $261; (b) $47