SOLUTION: A truck can be rented from Company A for ​$80 a day plus ​$0.40 per mile. Company B charges ​$50 a day plus ​$0.90 per mile to rent the same truck. Find the number of miles

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Question 1203527: A truck can be rented from Company A for ​$80 a day plus ​$0.40 per mile. Company B charges ​$50 a day plus ​$0.90 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same.
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52903) About Me  (Show Source):
You can put this solution on YOUR website!
.
A truck can be rented from Company A for ​$80 a day plus ​$0.40 per mile.
Company B charges ​$50 a day plus ​$0.90 per mile to rent the same truck.
Find the number of miles in a day at which the rental costs for Company A and Company B are the same.
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Use this equation

    80 + 0.40*m = 50 + 0.90*m,


where "m" denotes miles.


The origin of this equation is so clear that I will not spend your time for explanations.

Its left and right sides speak for themselves.


From the equation,

    m = %2880-50%29%2F%280.9-0.4%29 = 60.


ANSWER.  60 miles.


CHECK.  80 + 0.40*60 = 104 dollars = 50 + 0.9*60.    ! correct !

Solved.



Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

x = number of miles
y = total cost in dollars

Company A: y = 0.40x+80
Company B: y = 0.90x+50

Equate the right hand sides to solve for x.
0.90x+50 = 0.40x+80
0.90x-0.40x = 80-50
0.50x = 30
x = 30/0.50
x = 60

Driving 60 miles means the two costs are the same. Each cost is $104 because of the scratch work below.
y = 0.40x+80
y = 0.40*60+80
y = 24+80
y = 104
and also
y = 0.90x+50
y = 0.90*60+50
y = 54+50
y = 104
Both equations have x = 60 lead to y = 104


Answer: 60 miles