Expert: David Montiel - 8/26/2009

Question
The question is : A local department store is having a coupon sale in which you recieve $30 off any purchase over $50. a competing store is offering 30% off all purchases over $50. Write and graph two equations that describe the prices at both stores. When does the store offering the coupon sale have a better deal than their competitor? i am confused on how to make the two equations to graph.

Answer
Hello Jordan,

Before I get to your question, I should let you know that my policy is not to give full
solutions to questions like these because I believe it wouldn't really help you
learn. However I'll be glad to help you get started.

Each of the equations have to be written in separate parts. Let's consider the first case, where you get $30 off for any purchase over $50. Let's call "P" the price the customer has to pay, including the discount, and "R" the retail (regular) price.

So the first equation has two parts:

P = R,               if R < = $50,       ...(1a)
P = R - $30          if R > $50          ...(1b)

where the symbol "< =" denotes "less or equal than". So to plot this you have to consider two separate instances: when "R" is less or equal than $50 (1a) and when it is more then $50 (1b).

In the second case you have

P = R,                 if R < = $50,       ...(2a)
P = R - 0.3*R          if R > $50          ...(2b)

You plot this the same way you did for the first case.

I hope this helps,

Cheers,
David