A musician is planning to market a CD. The fixed costs are $1260 and the variable costs are $5 per CD. The wholesale price of the CD will be $11. For the artist to make a profit, revenues must be greater than costs.
How many CDs, x, must be sold for the musician to break even?
Solve this equation for x:
11x = 1260 + 5x
11x = 1260 + 5x
To find the number of CDs the musician must sell to break even, we need to determine the point at which revenue equals costs. In this case, the total revenue can be calculated by multiplying the number of CDs sold (x) by the wholesale price ($11), while the total costs include both fixed costs ($1260) and variable costs per CD ($5).
The equation can be written as:
Revenue = Total Costs
Let's establish the equation:
11x = 1260 + 5x
To solve for x, we need to isolate x on one side of the equation. First, let's combine like terms:
11x - 5x = 1260
Simplifying further:
6x = 1260
Now, divide both sides of the equation by 6:
x = 1260 / 6
Calculating the above expression:
x = 210
Therefore, the musician must sell 210 CDs in order to break even.