what amount is shown where the lines meet?

Question

Dr. Kim just got her PhD, and she wants to print copies of her thesis in hardcover book format. She could use Fairfax Printing, paying a setup fee of $50 and $5 for every book printed. Alternately, she could go through Burlington University, paying an up-front fee of $30 and $10 per book. It turns out that, given the number of books Dr. Kim wants to print, the two options cost the same amount. What is the amount?
Write a system of equations, graph them, and type the solution.

Answer 1

Anne, I hope I can still help.

 

So, for Fairfax, it's going to cost $50 plus $5 per book. If she does 2 books, then it's going to cost $50 + $5(2), so $60. If she does x books, it's going to cost $50 + $5x.

 

We write the term with the variable first, so our first equation is y = 5x + 50.

 

Using the same logic, the 2nd equation is y = 10x + 30.

 

To graph, we start with the y-intercepts and plot points from there with the slope.

 

Our first equation starts at 30 on the y-axis. The slope is 5, so we go up 5 and over 1, up 5 and over 1, etc. We don't go negative, since she can't print a negative number of books.

 

The 2nd equation is graphed in a similar fashion. Where the two lines cross is your answer. 

 

Hope this helps!

Answer 2

50 + 5x = 30 + 10x

 

5x = 20; x = 4 books

 

She'll spend $70 on her dissertations; a few years as a postdoc where she'll work 12 hours a day, 6 days a week; a couple years in abject poverty after her funding runs out; and then she'll land a satisfying career doing something that has nothing to do with her doctoral training.