31. A sports utility vehicle travels 386.4 miles on 14 gallons of gas. Which of the following represents the constant of proportionality in miles per gallon?
Answer: D
The constant of proportionality in miles per gallon is 27.6.
To find the constant of proportionality, we divide the total miles traveled by the number of gallons used. In this case, 386.4 miles divided by 14 gallons equals 27.6 miles per gallon.
A) 5,409.60
This option is incorrect as it represents an unrealistic figure for miles per gallon. The calculation of 386.4 miles divided by 14 gallons does not yield this number, making it an invalid choice.
B) 13.8
This option is also incorrect. If we divide 386.4 miles by 14 gallons, the result is not 13.8. This figure does not represent the actual miles per gallon, which is significantly higher.
C) 372.4
Option C is incorrect as well. The number 372.4 is not a reasonable representation of miles per gallon derived from the given distance and fuel consumption. The correct division produces a much lower value.
D) 27.6
This option is correct since it accurately reflects the result of dividing 386.4 miles by 14 gallons. This calculation shows that the vehicle achieves 27.6 miles for every gallon of gas consumed.
Conclusion
The correct answer, 27.6, represents the constant of proportionality in miles per gallon, accurately calculated from the given distance and fuel amount. All other options are either unrealistic or incorrect calculations based on the provided data, reinforcing that 27.6 is the only valid choice.