Question

What percent of $50$ is $5?$

Answer 1

Hint: We know that the percent of a number is expressed as a ratio to hundred. We know that we can express $x\%$ as $\dfrac{x}{100}.$ So, if we want to find $x\%$ of a number $n,$ then we can use the formula $\dfrac{x}{100}\times n.$

Complete step-by-step answer:
Let us consider the given problem.
We are asked to find what percent of $50$ is $5.$
Let us suppose that $5$ is $x\%$ of $50.$ Now, we need to find the value of $x.$
Since $5$ is $x\%$ of $50,$ we can express the relation using the formula given by $\dfrac{x}{100}\times n$ where this expression equals to the $x\%$ of the number $n.$
So, we will get $x\%$ of $50=\,\dfrac{x}{100}\times 50$
And from the question, we have $x\%$ of $50=5$
Now, we will equate the right-hand sides of the above equation to get $\dfrac{x}{100}\times 50=5.$
Here, $x$ is the only unknown variable to be found.
Now, to find the value of $x,$ we need to transpose the rest of the values from the left-hand side to the right-hand side of the equation. So, the equation will contain the unknown variable on one side of the equation and the known values on the other side of the equation.
When we transpose $50$ from the left-hand side to the right-hand side of the equation, it will get transposed to the denominator and when we transpose $100$ from the left-hand side to the right-hand side of the equation, it will get transposed to the numerator.
Then, we will get $x=\dfrac{5\times 100}{50}$
After cancelling the common factors, we will get $x=5\times 2=10.$
Hence $5$ is $10\%$ of $50.$

Note: If we are given with the percent $y$ of a number $n$ and asked to find what percent it is, we need to rearrange the above formula to $\dfrac{y\times 100}{n}.$ We obtain this formula by rearranging the formula for finding percent. Suppose that $x\%$ of a number $n$ is $y,$ then $\dfrac{x}{100}\times n=y$ and rearranging this formula will give $x=\dfrac{y\times 100}{n}.$