Question

A tin holds \[16\dfrac{1}{2}\] liters of oil. How many such tins will be required to hold \[313\dfrac{1}{2}\] liters of oil.

Answer 1

Hint: We will be making use of the unitary method concept to solve the question. To solve this question first of all determine the number of tins which are required to hold 1 liter of oil then we can easily multiply, \[313\dfrac{1}{2}=313.5\] liters to the obtained number to get the result.

Complete step-by-step answer:
We are given that a tin holds \[16\dfrac{1}{2}\] liters of oil. First of all we will convert this \[16\dfrac{1}{2}\] mixed fraction to normal fraction.
\[16\dfrac{1}{2}=\dfrac{16\times 2+1}{2}=\dfrac{33}{2}=16.5\]liters.
So a tin can hold 16.5 liters of oil.
Hence the capacity of a tin is 16.5.
We have to calculate how many such tins would be required to hold \[313\dfrac{1}{2}\] liters of oil.
Now again we convert \[313\dfrac{1}{2}\] to fraction.
\[313\dfrac{1}{2}=\dfrac{313\times 2+1}{2}=\dfrac{626+1}{2}=313.5\]
Therefore we need to determine the number of tin required to hold \[313\dfrac{1}{2}=313.5\] liters of oil.
Now, let us apply the unitary method as shown below,
1 tin holds = 16.5 liters of oil.
\[\Rightarrow \] 16.5 liters of oil = 1 tin.
\[\Rightarrow \] 1 liter of oil = \[\dfrac{1}{16.5}\] tin.
\[\Rightarrow \] 1 liter of oil = 0.0606060 tin.
Now as we have to determine number of tin required for 313.5 liters then multiplying 313.5 in above we get,
313.5 liters = 0.0606060 \[\times \] 313.5
313.5 liters = 18.99999
313.5 liters \[\approx \] 19 tins
Now we have that the number of tins required to hold 313.5 liters of oil is 18.99999 tins which is approximately equal to 19 tins.
Hence to hold \[313\dfrac{1}{2}\] liters of oil 19 tins are needed.

Note: Since we have been given \[16\dfrac{1}{2}\] and \[313\dfrac{1}{2}\] as mixed fractions, we could have easily written them as 16.5 and 313.5. Since we know that \[\dfrac{1}{2}\] is 0.5. So, the step of converting them into normal fractions can be avoided. We can also solve the last part of the solution by not converting to decimals and simplifying the fractions as,
\[\begin{align}
  & =\dfrac{1}{16.5}\times 313.5 \\
 & =\dfrac{313.5}{16.5} \\
 & =\dfrac{3135}{165} \\
 & =19 \\
\end{align}\]