The Pennyweight Movie Club lets you buy a dozen DVDs for a penny on the conditions that you purchase at least 20...

Question

The Pennyweight Movie Club lets you buy a dozen DVDs for a penny(.01) on the conditions that you purchase at least 20 more DVDs for $17.99 each over the course of the year.

 

a. Write an ordered pair described by the information.

b. Write the slope described by the information.

c. Find an equation relating y, the total cost of purchasing the DVDs, to x, the number of DVDs you purchase.

d. Determine the cost of purchasing the required number of DVDs (12 plus 20 for a total of 32 DVDs).

Answer 1

The Pennyweight Movie Club lets you buy a dozen DVDs for a penny(.01) on the conditions that you purchase at least 20 more DVDs for $17.99 each over the course of the year.
 
a. Write an ordered pair described by the information.

 

You are in compliance with the terms when you join the club and buy 12 DVD's [Let x = number of DVD's and y = the total cost, see (c) below] for $0.01.  So, one point is (12, $0.01).

b. Write the slope described by the information.

 

The slope indicates the rate of increase in cost for each additional DVD (given by the problem as $17.99 each). 

 

c. Find an equation relating y, the total cost of purchasing the DVDs, to x, the number of DVDs you purchase.

 

     y = $0.01 + $17.99(x-12)       [note: this is $0.01 for 12 plus $17.99 for "additional" over 12]

     y = $17.99x - $215.87 [also, x>= 32]

d. Determine the cost of purchasing the required number of DVDs (12 plus 20 for a total of 32 DVDs).

 

     Here, x = 32

     y = $0.01 + $17.99(32-12)             [You could use either equation]

     y = $0.01 + $17.99(20)            [$0.01 to start + $17.99 each for 20 more]

     y = $359.81