Comparison of On-line Rates

Date: 5/20/96 at 21:47:53
From: Nick Magee
Subject: Help!

I just took the Golden State Exam. I need the answer to a question:
 
Jack is interested in two on-line companies. Easy Comp. offers a base 
rate of $10 and the first 2 hours free. Each additional hour is $4 
extra. Destruct Comp. offers a base rate of $8 and the first 5 hours 
free. Each additional hour is $5 extra. 

When will the prices be the same at the same hour?

I get 16 hours.

   Thank You,
       Nick Magee

Date: 6/14/96 at 1:7:2
From: Doctor Paul
Subject: Re: Help!

Sorry Nick..The answer is 19 hrs. :-(  

Here's how to do it: set it up using algebra...

Base Rate + (Fee Per hour)(Hours over 2) 
          = Base Rate + (Fee Per hour)(Hours over 5)

Which in numbers is

10 + 4(x-2) = 8 + 5(x-5)
10 + 4x - 8 = 8 + 5x - 25
2 + 4x = 5x - 17
19 = x

So the answer is 19 hrs.  This is very easy to check...
Easy comp:  10 + 4(19-2) = 78 dollars
Dstct comp:  8 + 5(19-5) = 78 dollars

Hope this helps..

-Doctor Paul,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/