Question

Ryan is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices. Company A charges an initial fee of $72.50 and an additional 40 cents for every mile driven. Company B charges an initial fee of $25 and an additional 90 cents for every mile driven. For what mileages will Company A charge no more than Company B? Write your answer as an inequality, using m for the number of miles driven.

Answer 1

m≥95

Explanation:

Since, we have two option given.

forming the equation for Company A

As company A pay fixed (intercept) of $72.5. Moreover, with every one mile driven company A pays $0.4 (slope)

Using the equation

y=mx+c

where m is slope, and c is intercept.

In the case of company A. slope is $0.4, and intercept is $72.5.

charges= 0.4m+72.5

Forming the equation for company B

charges=0.9m+25

Now, as per the requirement of question we must find the value of m, where Company A will charge no more than company B

That means,

we have to find the value of m where charges from equation of company A should be less than or equal to charges from equation of company B

in other words,

0.4m+72.5 ≤ 0.9m+25

solving for m,

Step 1

72.5-25 ≤  0.9m-0.4m

Step 2

47.5≤ 0.5m

Step 3

47.5/0.5≤ m

Step 4

95≤ m

in other words, m≥95