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.