Question

A full glass of water can hold $\dfrac{1}{6}$ of a bottle. How many glasses of water can be filled with $3\dfrac{1}{2}$ bottles of water?

Answer 1

Hint: Try to find how many glasses will fill a bottle from the given question. The question has given us the amount of water a glass can have with respect to a bottle. But we will use this information to get how many glasses can fill 1 single bottle. After getting that number we will multiply that number with $3\dfrac{1}{2}$ which will give us our answer.

Complete step by step solution:
Here, in the question it is given that $\dfrac{1}{6}$ of a bottle is filled in a glass
Therefore, we can easily say that 6 glasses will have the capacity to fill a bottle.
As, $\dfrac{1}{6}$bottle $ \times $6=6 bottles
Hence, if 1 bottle has 6 glasses of water in it. $3\dfrac{1}{2}$ will have
\[3\dfrac{1}{2} \times 6 = \dfrac{7}{2} \times 6 = 7 \times 3 = 21\]glasses
\[\left\{ {\because \,3\dfrac{1}{2} = \dfrac{{(3 \times 2) + 1}}{2} = \dfrac{7}{2}} \right\}\]
Therefore, if 1 glass has $\dfrac{1}{6}$ bottle of water, then $3\dfrac{1}{2}$bottles of water will be filled with 21 glasses of water.

Note: The given mixed fraction $3\dfrac{1}{2}$ should be calculated carefully, as the simplified form of These types $(x\dfrac{y}{z})$ of mixed fractions have the solution as $\dfrac{{(z \times x) + y}}{z}$. The multiplication and summation should be of the same order and should not be mixed or forgotten as this will be used many times in future too. Another point to remember is that you must calculate the fractions carefully as in the solution we are finding how many glasses will fill a bottle and not how many bottles will be glass.