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 (such as printing). There are two production methods it could use. With one method, the one-time fixed costs will total
$12,303
, and the variable costs will be
$18.50
per book. With the other method, the one-time fixed costs will total
$42,135
, and the variable costs will be
$10.25
per book. For how many books produced will the costs from the two methods be the same?

Answer 1

@ksanka

Answer 2

Method 1 Method 2
fixed cost 1 + variable cost 1 = fixed cost 2 + variable cost 2

Answer 3

$18.50 will be the fixed cost right?

Answer 4

Use the equation above.
First, replace the fixed costs with the correct amounts that are given to you.

Answer 5

You need to read the problem carefully.
It says clearly that the fixed costs are
Method 1: $12,303, and
Method 2: $42,135

Answer 6

In the equation I wrote above, replace the two fixed costs with the numbers i just gave you.

Answer 7

12,303+$18.50 = $42,135+$10.25

Answer 8

@ksanka

Answer 9

Not quite.
SO far, you should only have the fixed costs.
I haven't told you yet what to do with the variable costs.
You should have this now:

$12,303 + variable costs 1 = $42,135 + variable costs 2

Answer 10

Now let's see how we deal with the variable costs.

Answer 11

ok.

Answer 12

A variable cost is a cost that varies, or changes, depending on something.
In this case, the variable costs vary according to how many books are being printed.

Answer 13

ok.

Answer 14

For the first method, the variable cost is $18.50 per book.

If you print 1 book, the cost is $18.50 * 1
If you print 2 books, the cost is $18.50 * 2

We don't know how many books will be printed, so we use the variable x to represent the number of books.
If you print x books, the variable cost will be $18.50 * x, or 18.5x
All of the above is the variable cost for method 1.

Answer 15

18.5x

Answer 16

Now we have this:

$12,303 + 18.5x = $42,135 + variable costs 2

Answer 17

Exactly.

Answer 18

Now we look at the variable costs for the second method.
In that method, the variable cost is $10.25 per book.
How much would it cost to print x books?

Answer 19

10.2x

Answer 20

Exactly.
Now we substitute that into our equation, and our equation will be ready to be solved.

$12,303 + 18.5x = $42,135 + 10.25x

Answer 21

We set the prices of the two methods equal because the question asks for how many books will the cost be the same.

Answer 22

ok.

Answer 23

Now we solve the equation for x.
Do you need help with that?

Answer 24

yes

Answer 25

I drew the equation below because it looks more like it will look in your notebook.