A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). The one-time fixed costs will total $45,920. The variable costs will be $11.25 per book. The publisher will sell the finished product to bookstores at a price of $21.50 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?

Number of books sold is variable. To get the amount earned from sales equal to total production cost, publisher must produce 4480 books.

How to form mathematical expression from the given description?

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

For the given case, we will use variable in place of the number of books sold. Variables can be used in place of quantities whose values isn't fixed constant number, or is unknown.

Let we have:

Number of books sold to get the earned money from sales equal to production cost = [tex]x[/tex] books

Now, We need to calculate the total production cost.

Total production cost by selling [tex]x[/tex] books = Fixed one time cost + Cost for production of [tex]x[/tex] books.

Since fixed one time cost = $45,920,

and cost for production of each book = $11.25, thus,

cost for production of [tex]x[/tex] books is [tex]11.25 \times x[/tex] (in dollars).

Thus,

Total production cost = [tex]11.25x + 45920[/tex] (in dollars)

The amount earned by selling 1 book = $21.50

Amount earned by selling [tex]x[/tex] books = [tex]21.5 \times x[/tex] (in dollars)

Since they need to be same, equating them, we get:

[tex]\text{Total production cost = Total amount earned from sales of x books}\\11.25x + 45920 = 21.5x\\\\\text{Subtracting 11.25x from both the sides}\\\\45920 = (21.5-11.25x)\\45920 = 10.25x\\\\\text{Dividing both the sides by 10.25}\\\\\dfrac{45920}{10.25} = \dfrac{10.25x}{10.25}\\\\4480 = x\\x =4480[/tex]

Thus, publisher must produce x = 4480 books.

Thus,

Learn more about forming equations here:

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