Question

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 (suchas printing). The one-time fixed costs will total $60,480. The variable costs will be $10.75 per book. The publisher will sell the finished product to bookstores ata price of $25.75 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?

Answer 1

Let 'n' represents the number of books.

Let 'F' represents the one-time fixed cost

Let 'V' represents the variable cost

Let 'S' represents sales cost

Let's write out the equation

`\begin{gathered} \text{where F=\$60,480} \\ V=\text{ \$10.75}* n=\text{ \$10.75n} \\ S=\text{ \$25.75}* n=\text{ \$25.75n} \end{gathered}`

`\begin{gathered} F+\text{ V=S} \\ \text{ \$60,480+\$10}.75n=\text{ \$25.75n} \\ \text{ \$60,480=\$25.75n-\$10.75n} \\ \end{gathered}`
`\begin{gathered} \text{ \$60,480=\$15}n \\ \text{Divide both sides by \$15} \\ \frac{\text{ \$60,480}}{\text{ \$15}}=\text{ }\frac{\text{\$15n}}{\text{ \$15}} \\ 4032=n \end{gathered}`

Hence, the number of books that the producer must produce and sell so that the production costs will be equal to the money from sales is 4032books.