If Tammy gives Cody $38, the amount of money she has will be 10% of his. If Cody gives Tammy $169, he will have the same amount of money as her. How much money did each of them have?
(a) Cody
(b) Tammy
|
Case 1 |
Case 2 |
|
Cody |
Tammy |
Cody |
Tammy |
Before |
10 u - 38 |
1 u + 38 |
5.5 u + 169 |
5.5 u - 169 |
Change |
+ 38 |
- 38 |
- 169 |
+ 169 |
After |
10 u |
1 u |
5.5 u |
5.5 u |
(a)
10% =
10100 =
110 In Case 1, when Tammy gives to Cody, there is an internal transfer of money from Tammy to Cody. The total amount that both have remains the same.
In Case 2, when Cody gives to Tammy, there is an internal transfer of money from Cody to Tammy. 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 Tammy and Cody have
= 10 u + 1 u
= 11 u
Amount that Tammy 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 - 38 = 5.5 u + 169
10 u - 5.5 u = 169 + 38
4.5 u = 207
1 u = 207 ÷ 4.5 = 46
Amount that Cody has
= 10 u - 38
= 10 x 46 - 38
= 460 - 38
= $422
(b)
Amount that Tammy has
= 1 u + 38
= 1 x 46 + 38
= 46 + 38
= $84
Answer(s): (a) $422; (b) $84