1. The equation d/f = g represents gallons of gasoline used, g, in terms of distance traveled in miles, d, and fuel efficiency, / miles per gallon of gasoline. Which combination of distance traveled and fuel efficiency uses 3 gallons of gasoline?
Answer: B
57 miles and 19 miles per gallon uses 3 gallons of gasoline.
By substituting the values from Option B into the equation d/f = g, we can determine that 57 miles divided by 19 miles per gallon equals approximately 3 gallons of gasoline used.
A) 7 miles and 21 miles per gallon
Substituting these values into the equation gives 7/21, which simplifies to 1/3, indicating that this combination uses only about 0.33 gallons of gasoline, not 3 gallons. Therefore, this option is incorrect.
B) 57 miles and 19 miles per gallon
Using the equation, we calculate 57 miles divided by 19 miles per gallon, which equals exactly 3 gallons. This combination accurately reflects the relationship described in the equation, making it the correct choice.
C) 23 miles and 20 miles per gallon
Calculating with these numbers, we find 23/20 equals 1.15 gallons of gasoline used. This is significantly less than 3 gallons, indicating that this option does not meet the criteria.
D) 32 miles and 35 miles per gallon
For this combination, 32 miles divided by 35 miles per gallon results in approximately 0.91 gallons of gasoline. This value is well below the required 3 gallons, thus making this option incorrect.
Conclusion
Option B is definitively correct as it satisfies the equation by yielding exactly 3 gallons of gasoline used. In contrast, Options A, C, and D do not meet the requirement of using 3 gallons, proving them to be incorrect alternatives.