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algebra word problem

Mathematics
Tutor: None Selected Time limit: 1 Day

What equation do I use for the following algebra word problem? Ace car rental $25 daily+.10 cents a mile and Better car rental $40 daily+.05 cents a mile. For what number of miles is the cost of renting a car the same at both companies?

Mar 17th, 2015

The first part of this question is writing two equations to represent the cost of renting a car from the two companies.  If you need additional practice on writing equation and expressions from word problems, check out the two links below.  Both have examples and practice problems as well as a list of keywords to look for.

http://www.purplemath.com/modules/translat2.htm

http://www.mathgoodies.com/lessons/vol7/equations.html

For this problem let us first define our variables:

C =  total cost of renting a car

d = distance traveled

Ace : C = 0.10d + 25

Better : C = 0.05d + 40

With these two equations, we are now looking for a distance at which the cost is equal. 

This means that C will be the same in both equations, so we can say that

0.10d + 25 = 0.05d + 40

Then you can use this new equation to solve for the distance at which cost is equal for both comanies

0.10d + 25 = 0.05d + 40

-0.05d            -0.05d

0.05d + 25 = 40
            -25     -25
0.05d = 15
d = 15 / 0.05 
d = 300 miles
C = 0.10*300 + 25
C = 30 + 25 
C = $55.00
At a distance of 300 miles, both rental cars would cost $55.00.
If you have any additional questions or require clarification, please let me know.

Mar 17th, 2015

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