London is deciding between two truck rental companies. Company A charges an initial fee of $40 for the rental plus $2.50 per mile driven. Company B charges an initial fee of $100 for the rental plus $1 per mile driven. Let A represent the amount Company A would charge if London drives x miles, and let B represent the amount Company B would charge if London drives x miles. Write an equation for each situation, in terms of x, and determine the interval of miles driven, x, for which Company A is cheaper than Company B.
A= B=
Company A is cheaper than company B when x (< or >)
(Dollars per mile, miles, dollars or miles per dollar)

An equation is an expression that shows the relationship between two or more numbers and variables. An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.

Let A represent the amount Company A would charge if London drives x miles, and let B represent the amount Company B would charge if London drives x miles.

For company A:

A = 2.5x + 40

Also, for company B:

B = x + 100

For Company A to be cheaper than Company B:

2.5x + 40 < x + 100

x < 40

Company A charges would be cheaper than company B if the number of miles driven would be less than 40 miles

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