Question

Ann is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices.

Company A charges $93 and allows unlimited mileage.
Company B has an initial fee of $65 and charges an additional $0.70 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

Ans: greater than 40 mileage Company A will charge less than Company B

Explanation:

as company A charges a fix amount $93 for any distance and company B charges variable amount starting from $65.there will be a certain mileage after that the amount charged by company B should be greater than company A.

let for greater than m mileage company A will

charge less than company B.

charge for company A for m mileage= $93

charge for company B for m mileage= $65 + $0.70*m

so,

93 ≤ 65+0.70*m

93-65 ≤ 65+0.70*m -65

28 ≤ 0.70*m

28*10 ≤ 7 *m

280 ≤ 7m

280/7 ≤ 7m/7

40 ≤ m

Answer 2

m>40

Explanation:

So, since we know that m is for the number of miles driven we can set up the following expressions.

Company A: 93+0m

Company B: 65+0.7m

Now that we know this, we can make it an inequality.

Company A<Company B

So:

93+0m<65+0.7m

0m is 0 so our inequality is now

93+0<65+0.7m

Now, we can subtract 65 from both sides.

93-65+0<0.7m

Combine like terms.

28<0.7m

Divide both sides by 0.7

40<m

So

m>40

This means that company A charges less for mileages over 40.