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Question 17 of 30

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M:C:MC:13

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The gas mileage for Peter’s car is 21 miles per gallon when the car travels at an average speed of 50 miles per hour. The car’s gas tank has 17 gallons of gas at the beginning of a trip. If Peter’s car travels at an average speed of 50 miles per hour, which of the following functions f models the number of gallons of gas remaining in the tank t hours after the trip begins?

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f left parenthesis t right parenthesis space equals space 17 space minus space fraction numerator 21 over denominator 50 t end fraction

Correct Answer: 
No

f left parenthesis t right parenthesis space equals space 17 space minus space fraction numerator 50 t over denominator 21 end fraction

Correct Answer: 
Yes

f left parenthesis t right parenthesis space equals space fraction numerator 17 space minus space 21 t over denominator 50 end fraction

Correct Answer: 
No

f left parenthesis t right parenthesis space equals space fraction numerator 17 space minus space 50 t over denominator 21 end fraction

Correct Answer: 
No

View Correct Answer

Choice B is correct. Since Peter’s car is traveling at an average speed of 50 miles per hour and the car’s gas mileage is 21 miles per gallon, the number of gallons of gas used each hour can be found by fraction numerator 50 space miles over denominator 1 space hour end fraction space cross times space fraction numerator 1 space gallon over denominator 21 space miles end fraction space equals space 50 over 21. The car uses 50 over 21 gallons of gas per hour, so it uses 50 over 21 t gallons of gas in t hours. The car’s gas tank has 17 gallons of gas at the beginning of the trip. Therefore, the function that models the number of gallons of gas remaining in the tank t hours after the trip begins is f left parenthesis t right parenthesis space equals space 17 space minus space fraction numerator 50 t over denominator 21 end fraction.

Choice A is not the correct answer. The number of gallons of gas used each hour is determined by dividing the average speed by the car’s gas mileage.

Choice C is not the correct answer. The number of gallons of gas used each hour is misrepresented as 21 over 50. Also, the number of gallons used each hour must be multiplied by time t before it is subtracted from the number of gallons of gas in the tank at the beginning of the trip.

Choice D is not the correct answer. The number of gallons of gas used each hour must be multiplied by time t before it is subtracted from the number of gallons of gas in the tank at the beginning of the trip.

Question Difficulty: 
medium
Objective: 

Students must create a function to represent a real-world situation.