Answer:
Each CD costs 8.00.
Each DVD costs 15.50.
Explanation:
- It appears you want to find the cost of each CD and each DVD.
- If so, my steps below will help you do this.
- If you're trying to find something else, write in the comments and I'll delete the answer below.
----------------------------------------------------------------------------------------------------------
We can determine the cost of each CD and each DVD using a system of equations, where,
- C represents the cost of each CD,
- and D represents the cost of each DVD.
First equation:
We know that the cost of 3 CDs and 6 DVDS is 117:
(3 * cost of CDs) + (6 * cost of DVDs) = 117
Thus, our first equation is given by:
3C + 6D = 117
Second equation:
We also know that the cost of 5 CDs and 3 DVDs is 86.5:
(5 * cost of CDs) + (3 * cost of DVDs) = 86.5
Thus, our second equation is given by:
5C + 3D = 86.5
Method to solve: Elimination:
Solving for C (i.e., the cost of each CD):
- First, we can multiply the second equation by -2.
This will allow us to eliminate D when we add it to the first equation since 6D - 6D = 0:
-2(5C + 3D = 86.5)
-10C - 6D = -173
Now we can add this equation to the first equation to eliminate D and solve for C:
3C + 6D = 117
+
-10C - 6D = -173
----------------------------------------------------------------------------------------------------------(3C - 10C) + (6D - 6D) = (117 - 173)
(-7C = -56) / -7
C = 8
Thus, each CD costs 8.00.
Solving for D (i.e., the cost of each DVD):
Now, we can solve for D by plugging in 8 for C in the first equation (i.e., 3C + 6D = 117):
3(8) + 6D = 117
(24 + 6D = 117) - 24
(6D = 93) / 6
D = 15.5
Thus, each DVD costs 15.50.