A software company is releasing one of its products on CD. The manufacturer charges a $5,500.00 setup fee and $1.00 per CD. Write an equation that can be used to find how many CDs must be produced for the total cost per CD to be $3.50.
A. 5500 + x over x = 3.50
B. 5500 over x plus x = 3.50
C. 5500 + 1 over x = 3.50
D. 5500 + x = 3.50 over x
you want totalcost/totalcds, so
(5500+x)/x = 3.50
I choose option E: None of the above!
Let's break down the problem:
The total cost consists of two parts: the setup fee and the cost per CD.
So we can express the total cost as the sum of these two components:
Total Cost = Setup Fee + (Cost per CD x Number of CDs)
Now, we're given that the setup fee is $5,500 and the cost per CD is $1.00. We want to find how many CDs must be produced for the total cost per CD to be $3.50.
Since we want to find the number of CDs, let's use 'x' to represent that variable. Therefore, the equation becomes:
5500 + (1.00 * x) = 3.50 * x
Simplifying it, we get:
5500 + x = 3.50x
And there you have it! The correct equation is:
5500 + x = 3.50x
The correct equation to find how many CDs must be produced for the total cost per CD to be $3.50 is:
C. 5500 + 1/x = 3.50
Explanation:
Let's break down the components of the problem:
- The manufacturer charges a $5,500.00 setup fee, which is a fixed cost that stays the same regardless of the number of CDs produced.
- There is an additional cost of $1.00 per CD. This is a variable cost that depends on the number of CDs produced. If x represents the number of CDs, then the additional cost would be 1/x.
To find the total cost per CD, we need to divide the total cost by the number of CDs produced:
Total Cost Per CD = (Setup Fee + Additional Cost) / Number of CDs
Based on the given information, the equation becomes:
(5500 + 1/x) / x = 3.50
Therefore, the correct equation is option C: 5500 + 1/x = 3.50.
To find the equation that can be used to determine the number of CDs needed for the total cost per CD to be $3.50, let's break down the problem.
We know that the manufacturer charges a setup fee of $5,500.00, which is a fixed cost. In addition to the setup fee, there is a variable cost of $1.00 per CD.
Let's assume the number of CDs to be produced is "x". The total cost (TC) can be calculated as the sum of the setup fee and the cost per CD multiplied by the number of CDs. Mathematically, it can be represented as:
TC = 5500 + 1x
To find the cost per CD, we divide the total cost by the number of CDs:
Cost per CD = TC / x
Now, we are given that the cost per CD should be $3.50. Therefore, we can set up the equation:
3.50 = (5500 + 1x) / x
Simplifying the equation, we get:
3.50x = 5500 + x
Combining like terms, we have:
3.50x - x = 5500
Simplifying further:
2.50x = 5500
To solve for x, we divide both sides of the equation by 2.50:
x = 5500 / 2.50
x = 2200
Therefore, the equation that can be used to find the number of CDs needed for the total cost per CD to be $3.50 is:
A. 5500 + x / x = 3.50