If Julie gives Cody $27, the amount of money she has will be 10% of his. If Cody gives Julie $117, he will have the same amount of money as her. How much money did each of them have?
(a) Cody
(b) Julie
|
Case 1 |
Case 2 |
|
Cody |
Julie |
Cody |
Julie |
Before |
10 u - 27 |
1 u + 27 |
5.5 u + 117 |
5.5 u - 117 |
Change |
+ 27 |
- 27 |
- 117 |
+ 117 |
After |
10 u |
1 u |
5.5 u |
5.5 u |
(a)
10% =
10100 =
110 In Case 1, when Julie gives to Cody, there is an internal transfer of money from Julie to Cody. The total amount that both have remains the same.
In Case 2, when Cody gives to Julie, there is an internal transfer of money from Cody 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 Cody have
= 10 u + 1 u
= 11 u
Amount that Julie and Cody each has in the end for Case 2
= 11 u ÷ 2
= 5.5 u
Amount that Cody has at first is the same in Case 1 and Case 2.
10 u - 27 = 5.5 u + 117
10 u - 5.5 u = 117 + 27
4.5 u = 144
1 u = 144 ÷ 4.5 = 32
Amount that Cody has
= 10 u - 27
= 10 x 32 - 27
= 320 - 27
= $293
(b)
Amount that Julie has
= 1 u + 27
= 1 x 32 + 27
= 32 + 27
= $59
Answer(s): (a) $293; (b) $59