Question

What percent of $68$ is $17?$

Answer 1

Hint: We know that when we need to find the $x\mathrm{\%}$ percent of a number $n,$ we can use the formula ${\displaystyle \frac{x}{100}}\times n=y$ and $y$ is the $x\mathrm{\%}$ of the number $n.$ So, if we are given with the percent $y$ of a number $n$ and asked to find what percent it is, we can use the formula $x={\displaystyle \frac{y\times 100}{n}}.$

Complete step-by-step solution:
Let us consider the given problem.
We are asked to find what percent of $68$ is $17.$
Let us suppose that $17$ is $x\mathrm{\%}$ of $68.$ Now, we need to find the value of $x.$
Since $17$ is $x\mathrm{\%}$ of $68,$ we can express the relation using the formula given by ${\displaystyle \frac{x}{100}}\times n$ where this expression equals to the $x\mathrm{\%}$ of the number $n.$
So, we will get $x\mathrm{\%}$ of $68={\displaystyle \frac{x}{100}}\times 68$
And from the question, we have $x\mathrm{\%}$ of $68=17$
Now, we will equate the right-hand sides of the above equation to get ${\displaystyle \frac{x}{100}}\times 68=17.$
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 $68$ 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 $x={\displaystyle \frac{17\times 100}{68}}$
After cancelling the common factors, we will get $x={\displaystyle \frac{17\times 50}{34}}={\displaystyle \frac{50}{2}}=25.$
Hence $17$ is $25\mathrm{\%}$ of $68.$.

Note: When we discuss the percent of a number $n,$ we write the number in terms of hundred. When we say $x\mathrm{\%},$ we mean to say the ratio ${\displaystyle \frac{x}{100}}.$ So, the phrase $x\mathrm{\%}$ of a number $n$ is $y$ can be expressed Mathematically as ${\displaystyle \frac{x}{100}}\times n=y.$