Final answer:
The bin's capacity is found using a proportion, showing that if 1/8 gallon fills 2/3 of the bin, then 3/16 gallon would fill the whole bin. Thus, the answer is 3/16 gallon.
Step-by-step explanation:
To find the bin's capacity, we need to determine how much water fills the entire bin if 1/8 gallon of water fills 2/3 of it. We set up a proportion where 2/3 of the bin is to 1/8 gallon as 1 whole bin (full capacity) is to 'x' gallons.
Let's solve this step-by-step:
\(2/3 \ of \ bin = 1/8 \ gallons\)
Therefore, \(1 \ of \ bin = (1/8) / (2/3) \ gallons\)
Next, we calculate that:
\(1 \ bin = (1/8) \times (3/2) \ gallons \)
\(1 \ bin = 3/16 \ gallons\)
So, the bin's capacity is \(3/16\) gallons, which corresponds to choice \(b\).