Question

The average cost of an item is defined as the total cost toproduce it divided by the number of units produced. A shoecompany that pays $240, 000 in rent and employee salaries peryear figures it also must pay $3.50 in materials per shoe set itproduces.Write an equation that represents how many shoe sets thecompany would need for the average cost to be $7.50.

Answer 1

The equation that represents how many shoe sets the company would need to produce for the average cost to be $7.50 is

7.5x = 240,000 + 3.5x

Solving this, we obtain that the company needs to produce 60,000 shoe sets for the average cost to be $7.50.

Step-by-step explanation

The question wants us to write an equation that will represent the number of shoe sets the company would need to produce for the average cost to be $7.50

Let this number of shoe sets be x,

The average cost = (Total Cost) ÷ (Number of shoe sets produced)

The average cost = 7.50 dollars

The total cost for this company can be calculated from the information given that the company pays $240,000 in rent and employee salaries and an extra $3.50 for each shoe set produced.

To produce x shoe sets, the extra cost will be

$3.50 × x = 3.5x dollars

So,

The total cost = (240,000 + 3.5x) dollars

Number of shoe sets produced = x

The average cost = (Total Cost) ÷ (Number of shoe sets produced)

7.50 = (240,000 + 3.5x) ÷ x

`\begin{gathered} 7.5\text{ = }(240000+3.5x)/(x) \\ \text{Cross multiply} \\ 7.5* x=240000+3.5x \\ 7.5x=240000+3.5x \end{gathered}`

Hence, the equation that represents how many shoe sets the company would need to produce for the average cost to be $7.50 is

7.5x = 240,000 + 3.5x

Solving this,

7.5x - 3.5x = 240,000

4x = 240,000

Divide both sides by 4

(4x/4) = (240,000/4)

x = 60,000 shoe sets.

Hope this Helps!!!