Question

Find the number whose \[12\dfrac{1}{2}\]% is 64?

Answer 1

 Hint: Percentage of a number represents the ratio of the number as a part of 100. A percentage is converted into its decimal equivalent by multiplying the numerical value of percentage by 100. In general, $a\% = a \times 100$. Here, the formula used is \[a \times \dfrac{b}{{100}} = c\] where $a$ is the number whose percentage to be found and $b$ is the percentage use-value.

Complete step-by-step answer:
Let \[x\] be the number whose \[12\dfrac{1}{2}\% \] is given by 64.
A mixed fraction of the form $a\dfrac{b}{c}$ (where $a$ is called as the quotient or whole number, $b$ is called as the remainder when divided by the number$c$) is converted into proper fraction as $a\dfrac{b}{c} = \dfrac{{ac + b}}{c}$.
Here, the percentage given is in mixed fraction form, convert it into proper fraction as:
\[12\dfrac{1}{2} = \dfrac{{\left( {12 \times 2} \right) + 1}}{2} = \dfrac{{24 + 1}}{2} = \dfrac{{25}}{2}\]
So, we can represent \[12\dfrac{1}{2}\% \] as \[\dfrac{{25}}{2}\% \]
Now, to get the result substitute $a = \dfrac{{25}}{2},b = x$ and $c = 64$ in the formula \[a \times \dfrac{b}{{100}} = c\]
We get, \[\dfrac{x}{{100}} \times \dfrac{{25}}{2} = 64\]
Solving the relation in terms of $x$ by cross multiplying the terms by multiplying the denominator terms of the left-hand side to the numerator of the right-hand side and the numerator terms of the left-hand side to the denominator of the right-hand side by keeping all the variable parameter to the left-hand side only, we get:
\[
  x = \dfrac{{64 \times 2 \times 100}}{{25}} \\
   = \dfrac{{1280}}{{25}} \\
   = 512 \\
 \]
Hence, the number whose \[12\dfrac{1}{2}\% \] is 64 is 512. In other words, it can also be written that \[12\dfrac{1}{2}\% \]of 512 is 64.

Note: Convert a mixed fraction into proper fraction whenever it is given in the question for easy to understand and remove the chances of error.