A 96-mile trip requires 6 gallons of gasoline. At this rate, what is the least number of gallons required for a 160-mile trip?

Rationale

10 gallons of gasoline are required for a 160-mile trip.

To determine the amount of gasoline needed for a 160-mile trip based on the given rate, we first calculate the fuel efficiency from the initial trip of 96 miles using 6 gallons. This gives us a rate of 16 miles per gallon. Thus, for 160 miles, the required gasoline can be computed as 160 miles divided by 16 miles per gallon, resulting in 10 gallons.

A (8) YOUR ANSWER

This choice suggests that only 8 gallons would be sufficient for the 160-mile trip, implying a fuel efficiency of 20 miles per gallon. However, this is incorrect as the calculated fuel efficiency from the original trip is only 16 miles per gallon.

B (10) CORRECT

This choice accurately reflects the calculation based on the fuel efficiency of 16 miles per gallon. By dividing 160 miles by this rate, we find that 10 gallons are indeed necessary for the trip, making this the correct answer.

C (12) YOUR ANSWER

Selecting 12 gallons would indicate a fuel efficiency of approximately 13.33 miles per gallon for the 160-mile trip. This is not supported by the initial rate of 16 miles per gallon, which clearly shows that more fuel is not required than calculated.

D (15) YOUR ANSWER

Choosing 15 gallons suggests an inefficient rate of 10.67 miles per gallon for the 160-mile trip. This option exceeds the necessary amount derived from the original trip's fuel efficiency, leading to an overestimation.

E (16) YOUR ANSWER

This option implies a fuel efficiency of 10 miles per gallon for the 160-mile trip, which is significantly lower than the established rate of 16 miles per gallon. Therefore, this amount is unnecessarily high for the distance traveled.

Conclusion

The correct calculation of gasoline required for a 160-mile trip, based on the initial trip's fuel efficiency, confirms that 10 gallons is the least amount needed. All other options either underestimate or overestimate fuel consumption, failing to align with the established efficiency rate of 16 miles per gallon. This reinforces the importance of accurate calculations in determining resource needs for travel.

A 96-mile trip requires 6 gallons of gasoline. At this rate, what is the least number of gallons required for a 160-mile trip?

10 gallons of gasoline are required for a 160-mile trip.

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