Question

~~Will give a medal!!~~

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 $44,022. The variable costs will be $9 per book. The publisher will sell the finished product to bookstores at a price of $25.50 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?

Answer 1

@FortyTheRapper

Answer 2

So we want:

\[Fixed +Variable=Sales\]

They've gave you all 3 of these values, do you see them in the paragraph?

Answer 3

uuuuuummmm no

Answer 4

oh actually yes

Answer 5

44,022 + 9 = 25.50

Answer 6

@FortyTheRapper

Answer 7

That's perfect.

Now let x = books

The only values in the problem that mention per book is the 9 and 22.50, so we can conclude.

\[9x + 44,022 = 25.50x\]

Now we can go back to classic algebra and solve for X to find our answer.

Answer 8

is it 1,726? @FortyTheRapper

Answer 9

I'm not getting that. Let's see:

So first, we subtract 9x from both sides
\[44,022 = (25.50x - 9x) = 16.50x\]

Then we divide both sides by 16.50x

\[\frac{ 44,022 }{ 16.50 } = x\]

Answer 10

oh 2,668 :O

Answer 11

That's what I got.

2,668 books need to be sold to equal the production cost

Answer 12

can you help me with one more? @FortyTheRapper

Answer 13

Sure

Answer 14

Customers of a phone company can choose between two service plans for long distance calls. The first plan has a $12 monthly fee and charges an additional $0.19 for each minute of calls. The second plan has a $22 monthly fee and charges an additional
$0.14 for each minute of calls. For how many minutes of calls will the costs of the two plans be equal?

Answer 15

This one is slightly similar, but they gave us two plans

Let's look at the first plan to make an equation. So like the last one, the fixed cost is 12 and each minute is .19. Can you make an equation like we did the last question?

Let x = minutes

Answer 16

.19x + 12 = 22?

Answer 17

Almost. It would be just .19x + 12

22 is for the second equation. Would you know that one?

Answer 18

.14x + 22

Answer 19

Right!

Now they want to know when the prices will be equal, so... let's make them equal xD

\[.19x +12=.14x+22\]

Now we solve for x

Answer 20

oh boy this one looks harder :O

Answer 21

Let's take it one step at a time.
We need to get the numbers on one side, and the numbers with x on the other.

So, let's get the 12 on the other side first. How could we?

Answer 22

add it

Answer 23

We always want to do the opposite. In the equation is being added, so we would actually subtract it to get:

\[.19x = .14x+10 \] (Since 22-12 is 10)

Now we need to get .14x to the other side. Since it's a +.14, how can we get that to the other side?

Answer 24

subtract it from the 10 right?

Answer 25

We couldn't because the 10 doesn't have an x next to it

Answer 26

subtract it from the .19?

Answer 27

Yep, since those are like-terms. (.19 and .14 both have an x. We subtracted the 12 and 22 because they both didn't have an x)

So, now we get:

\[.05x = 10\]

Now we can do the last step and divide

\[x = \frac{ 10 }{ .05 }\]

Answer 28

200

Answer 29

Yep.

The prices will be the same when 200 minutes are used

Answer 30

thankk youu

Answer 31

You're welcome =)