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Inequality in One Variable Application: Rental Car Cost

Inequality in One Variable Application: Rental Car Cost


Hanna needs to rent a
car while on vacation. The rental company charges $18.95, plus 17 cents for each mile driven. If Hanna only has $40 to
spend on the car rental, what is the maximum number
of miles she can drive? Let’s first let the variable m equal the number of miles driven. And now let’s write an expression for the total cost of renting a car. Again, the company charges $18.95, plus 17 cents for each mile driven, which, in our case, would
be 17 cents times m. And therefore, the expression
for the total cost is 18.95 plus 0.17m. Again, this is $18.95 plus 17 cents times the
number of miles driven. And since Hanna only has $40
to spend on the car rental, this total cost must be
less than or equal to 40. And now let’s solve the inequality for m. The first step is to isolate the m term by adding or subtracting. To undo the positive 18.95, we subtract 18.95 on both
sides of the equation. Simplifying, 18.95 minus 18.95 is zero. The left side simplifies to 0.17m, which is less than or
equal to 40 minus 18.95, which is 21.05. And now for the last step,
we multiply or divide in order to solve for m. 0.17m means 0.17 times m. The last step is to
divide both sides by 0.17. Simplifying, 0.17 divided
by itself simplifies to one, one times m is m. We have m is less than or equal to 21.05 divided by 0.17. And let’s find this
quotient on the calculator. We need to careful
interpreting this though. Remember, m is the number of miles driven. Assuming Hanna cannot drive a fraction or decimal part of a mile, we would not round this up to 124. Because if we did, then the
cost would be more than $40. And therefore, we’re going
to round down to 123. And therefore, m, the
number of miles driven, must be less than or equal to 123. And therefore, Hanna can
drive a maximum of 123 miles without the cost of the
rental going over $40. I hope you found this helpful.

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