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?
57 miles and 19 miles per gallon uses 3 gallons of gasoline.
By substituting the values from option B into the equation \( g = \frac{d}{f} \), we find that \( g = \frac{57}{19} \approx 3 \) gallons, confirming that this combination of distance and fuel efficiency accurately results in 3 gallons of gasoline used.
Calculating the gallons used gives \( g = \frac{7}{21} \approx 0.33 \) gallons. This value is significantly less than 3 gallons, indicating that this combination would not consume the desired amount of gasoline.
For this option, substituting into the equation yields \( g = \frac{57}{19} \approx 3 \) gallons. This calculation shows that traveling 57 miles at a fuel efficiency of 19 miles per gallon indeed results in the use of 3 gallons of gasoline, making it the correct choice.
Using the equation, we find \( g = \frac{23}{20} = 1.15 \) gallons. This value is far below 3 gallons, indicating that this distance and fuel efficiency combination would also not meet the requirements.
Calculating for this option gives \( g = \frac{32}{35} \approx 0.91 \) gallons. Again, this value is significantly less than 3 gallons, confirming that this combination does not satisfy the condition.
The equation \( g = \frac{d}{f} \) allows us to determine the gallons of gasoline used based on distance and fuel efficiency. Among the given choices, only the combination of 57 miles traveled at 19 miles per gallon results in the use of exactly 3 gallons of gasoline, as shown through the calculations. The other options fall short, highlighting the importance of accurately applying the formula to derive the correct values.
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