SOLUTION: Ivan is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices. Company A charges an initial fee of $40 and an additi

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: Ivan is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices. Company A charges an initial fee of $40 and an additi      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 697408: Ivan is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices.
Company A charges an initial fee of $40 and an additional .80 cents for every mile driven.
Company B charges an initial fee of $53 and an additional .60 cents for every mile driven.
For what mileages will Company A charge less than Company B? Write your answer as an inequality, using m for the number of miles driven.



Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
First, I'll find the milage for which both
companies charge the same
Let +C+ = the charge for the day
given:
Company A:
(1) +C+=+40+%2B+.8m+
Company B:
(2) +C+=+53+%2B+.6m+
-------------------
Making the charges equal:
+40+%2B+.8m+=+53+%2B+.6m+
+.2m+=+53+-+40+
+.2m+=+13+
+m+=+65+
-----------
So, for 65 miles driven, the charge is the same
for both companies
I want to know if A charges less than B with
more miles driven or less miles driven.
What If I say +m+=+65.001+?
Company A:
(1) +C+=+40+%2B+.8m+
(1) +C+=+40+%2B+.8%2A65.001+
(1) +C+=+40+%2B+52.0008+
(1) +C+=+92.0008+
Company B:
(2) +C+=+53+%2B+.6m+
(2) +C+=+53+%2B+.6%2A65.001+
(2) +C+=+53+%2B+39.0006+
(2) +C+=+92.0006+
You can see that for slightly more than 65 miles driven,
B charges less than A. That means less than 65 miles
must be driven for A to charge less than B.
+m+%3C+65+ answer