Henry 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
$25
and an additional
80
cents for every mile driven.
Company B charges an initial fee of
$44
and an additional
60
cents for every mile driven.
For what mileages will Company A charge less than Company B?
A: cost = 25 + .8x
B: cost = 44 + .6x
set them equal to find out when the cost is the same.
then decide when A is cheaper
To determine the mileages at which Company A charges less than Company B, we need to compare the total cost for renting a truck from both companies for different mileages.
Let's start by determining the cost for renting a truck from Company A:
Cost (A) = Initial fee + (additional cost per mile * number of miles)
Given:
Initial fee for Company A = $25
Additional cost per mile for Company A = 80 cents = $0.80
So, the cost function for Company A can be written as:
Cost (A) = $25 + $0.80 * (number of miles)
Similarly, let's determine the cost for renting a truck from Company B:
Cost (B) = Initial fee + (additional cost per mile * number of miles)
Given:
Initial fee for Company B = $44
Additional cost per mile for Company B = 60 cents = $0.60
So, the cost function for Company B can be written as:
Cost (B) = $44 + $0.60 * (number of miles)
Now, we can set up the inequality to find the mileages at which Company A charges less than Company B:
Cost (A) < Cost (B)
$25 + $0.80 * (number of miles) < $44 + $0.60 * (number of miles)
Simplifying further:
$0.80 * (number of miles) - $0.60 * (number of miles) < $44 - $25
$0.20 * (number of miles) < $19
(number of miles) < $19 / $0.20
Therefore, Company A will charge less than Company B for mileages less than 95 miles.
To summarize, Company A will charge less than Company B for mileages less than 95 miles.