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Codi Bender
8th Grade
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ASSESSMENT
Question Id : 58823
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Question
Joseph is going on a trip and he needs to rent a car. He looks online and finds two companies that offer different pricing options for car rentals. Company A charges $0.25 per mile plus a $50 rental fee. Company B charges $0.45 per mile plus a $20 rental fee.
What is the maximum number of miles that Joseph can drive in order for Company B to be a better buy? The company charges only for whole number mileage (not fractional increments of miles driven).
Responses
A 125 miles125 miles
B 149 miles149 miles
C 150 miles150 miles
D 151 miles
To determine the maximum number of miles that Joseph can drive for Company B to be a better buy, we need to calculate the cost for both companies at different mileage points until the cost for Company B exceeds Company A's cost.
For Company A:
Cost = $0.25 per mile + $50 rental fee
For Company B:
Cost = $0.45 per mile + $20 rental fee
Let's calculate the cost for both companies at different mileage points and find the maximum mileage at which Company B is a better buy.
For Company A:
50 + 0.25x (where x is the number of miles driven)
For Company B:
20 + 0.45x (where x is the number of miles driven)
Setting the cost for Company B greater than Company A, we have:
20 + 0.45x > 50 + 0.25x
Simplifying the equation:
0.2x > 30
x > 150
Therefore, the maximum number of miles that Joseph can drive for Company B to be a better buy is 150 miles.
So, the correct answer is C) 150 miles.