Question 31

A fully filled bucket contains 6 4/5 gallons of water.

To find the total capacity of the bucket, we can use the information that 2 4/5 gallons represents 1/3 of the total capacity. By multiplying 2 4/5 by 3, we determine that the fully filled bucket contains 6 4/5 gallons.

A) 14/15

This option is incorrect because 14/15 is significantly less than the actual total capacity of the bucket. When converted to a decimal, it is approximately 0.93 gallons, which does not reflect the volume of water when the bucket is 1/3 full.

B) 8 2/5

While this option is a plausible quantity, it is incorrect. To determine the total bucket capacity, one must multiply the 1/3 full volume (2 4/5 gallons) by 3. This calculation does not yield 8 2/5 gallons, as it exceeds the correct total.

C) 6 4/5

This is the correct answer. By calculating the total capacity of the bucket as 2 4/5 gallons multiplied by 3, we find the complete volume is indeed 6 4/5 gallons. This aligns with the initial information provided regarding the bucket's fullness.

D) 2 7/15

This option is incorrect. The value 2 7/15 is less than the volume that represents 1/3 of the bucket's total capacity. It does not correspond to the calculations derived from the volume of water when the bucket is only 1/3 full.

Conclusion

The accurate total capacity of the bucket is determined to be 6 4/5 gallons, as calculated from the given volume that represents 1/3 of its total capacity. All other options either underestimate or misrepresent the total volume, confirming that option C is the only correct answer.