How to Determine the Capacity of a Mug

Question:

A mug is ⅕ full. The mug contains ⅜ of a cup of water. Find the capacity of the mug.

Answer:

The capacity of the mug is 1/2 cup.

To determine the capacity of the mug, follow these steps:

1. Calculate the remaining portion of the mug that is not filled with water. Since the mug is ⅕ full, the remaining portion is 4/5.
2. Correlate the remaining portion of the mug with the amount of water it contains. In this case, the mug contains ⅜ of a cup of water.
3. Set up a proportion to find the capacity of the mug. Since 1 cup is equivalent to 5/8 cup (⅜ of a cup + remaining 4/5 of the mug), the capacity of the mug is represented by x.
4. Solve the proportion to find the capacity of the mug:

   1 cup is to 5/8 cup as x (capacity of mug) is to 4/5
   x = (5/8) * (4/5) = 20/40 = 1/2 cup

Therefore, the capacity of the mug is 1/2 cup.