Question

Lisa is going to rent a truck for one day. There are two companies she can choose from, and they have the following pricesCompany A charges $73 and allows unlimited mileage.Company B has an initial fee of $55 and charges an additional $0.90 for every mile driven.For what mileages will Company A charge less than Company B?Use m for the number of miles driven, and solve your inequality for m.

Answer 1

Hello there. To solve this question, we'll have to remember some properties about inequalities.

We know company A charges $73 and allows unlimited mileage, while company B has an initial fee of $55 and charges an additional $0.90 for every mile driven.

First, we want to find how many dollars Lisa would spend in each case:

With company A, she would only spend $73, since this is the cost and she can drive unlimitedly.

With company B, say m is the number of miles driven. Then Lisa would spend $55 from the initial fee and $ 0.90 multiplied by m, that is

$\ (55+0.90m)$

Now, we want to find the values of m satisfying the inequality such that company A charge less than company B, namely

$73<55+0.90m$

Subtract 55 on both sides of the inequality

$0.90m>18$

Multiply both sides by a factor of 10

$9m>180$

Divide both sides by a factor of 9

$m>20$

These are the values of m such that company A will charge less than company B.