Can you find the difference between the cost of a 15-line ad and a 17-line ad, without finding out the cost of each ad first? Explain.

Question

Mike is a veterinarian. He is placing a 9-line ad for an assistant. The following piece wise function gives the price of an x-line ad. a(x)=45 when x<3. a(x)=45+9(x-3) when x>3. Can you find the difference between the cost of a 15-line ad and a 17-line ad, without finding out the cost of each ad first? Explain.

Answer 1

Since the value of x is greater than 3 for both ads, we only need the second half of the piece wise function :

 

a(x)=45+9(x-3), we can simplify the function to:

 

a(x) = 45+9x-27

 

a(x) =18+9x

 

The difference between 15 and 17 is 2, and the only part of the equation to change is the 2x.  Substitute 2 for x and get 4, which is the difference in price for a 15 and 17 line ad.