Question

1. A college newspaper, The College Spy, has a fixed production cost of $70 per edition and it costs 40¢ per copy to print and distribute. The College Spy sells for 50¢ per copy.
a. What is the cost expression for the newspaper?


b. What is the revenue expression for the newspaper?


c. Put the cost and revenue expressions into an inequality that would represent a successful newspaper.



d. How many copies should be sold to make a profit? Show all work! An answer with no work will receive 0 points.







e. Now go back to your answer for d. On every line of your solution write what property of math you would use to justify the transformation that occurred.

Answer 1

a. What is the cost expression for the newspaper? 

The cost would be the sum of fixed cost and the variable cost. The fixed cost is 70 while the variable cost is 0.40 x, where x stands for the number of copies made. That is:

Cost = 70 + 0.40 x            

where x = number of copies made

b. What is the revenue expression for the newspaper? 

The revenue would simply be the product of selling price and number of copies sold or made, that is:

Revenue = 0.50 x

c. Put the cost and revenue expressions into an inequality that would represent a successful newspaper. 

To have a successful newspaper, the difference of revenue and cost must be greater than 0, that is:

Revenue – Cost > 0

0.50 x – (70 + 0.40 x) > 0


d. How many copies should be sold to make a profit? Show all work! An answer with no work will receive 0 points. 

From the above equation, we solve for x.

0.50 x – (70 + 0.40 x) > 0

0.50 x – 70 – 0.40 x > 0

0.10 x > 70

x > 700

Number of copies made should be more than 700 copies


e. Now go back to your answer for d. On every line of your solution write what property of math you would use to justify the transformation that occurred. 

 

0.50 x – (70 + 0.40 x) > 0                Distribution property

0.50 x – 70 – 0.40 x > 0                    Addition property

0.10 x > 70                                           Addition property

x > 700                                                  Division property