Question

Diane 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 $87 and allows unlimited mileage.
Company B has an initial fee of $75 and charges an additional $0.80 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

Let's see

For first one the fixed price is $87 and no extra charges

For second one fixed price is $75 and additional $0.8 for every mile

Equation

• y=0.8m+75

m is no of miles

Now

• 0.8m+75=87
• 0.8m=12
• m=12/0.8
• m=15

For 15 miles the cost will remain same

Answer 2

Less than 15 miles

m < 15

Explanation:

Given:

• Company A charges $87 and allows unlimited mileage.
• Company B has an initial fee of $75 and charges an additional $0.80 for every mile driven.

To find what mileages Company A will charge less than Company B, create an inequality where m is the number of miles driven:

⇒ Charge of Company A < Charge of Company B

⇒ 75 + 0.8m < 87

To solve the inequality:

75 + 0.8m < 87

Subtract 75 from each side:

⇒ 75 + 0.8m - 75 < 87 - 75

⇒ 0.8m < 12

Divide both sides by 0.8:

⇒ 0.8m ÷ 0.8 < 12 ÷ 0.8

⇒ m < 15

Therefore, Company A will charge less than Company B when the mileage is less than 15 miles.