Question

If 252 is 35% of a certain number, then find the number.

Answer 1

Hint: We have to find the whole number of the given partly value from the whole number. They give the partly value and percentage value of partly value. To solve this first we have to, consider the number asked to be a variable. Use the percentage formula to find the value of the variable which in turn gives you the value of the number.

Complete step-by-step solution:
Let the number to be found be \[x\]
Given,
\[35\% \] of the number is \[252\].
Substituting the assumed value in place of the given number, in the mathematical form, we get;
\[ \Rightarrow 35\% \] of \[x\] \[ = 252\]
Now, expanding the percentage, we get;
\[ \Rightarrow \dfrac{{35}}{{100}} \times x = 252\]
Here, any percentage when taken out is written as \[100\] in the denominator. Of simply means multiplication of the given two numbers or expressions.
By simplifying the above equation, i.e., we take the numerical value on the left-hand side to the right-hand side which becomes the reciprocal according to the algebraic rules. Doing that, we get;
\[ \Rightarrow x = \dfrac{{252 \times 100}}{{35}}\]
By dividing the numerator with the denominator, and cancelling out the common terms, we get;
\[ \Rightarrow x = 720\]

Therefore, the number to be found, that is, \[x = 720\]

Note: We have to mind that, a percentage is a fraction in which the denominator is \[100\]. To calculate a percentage, we have to use the percentage formula. The percentage formula is as given below:
\[P\% \times x = y\]
First, we need to convert any given problem in terms of the percentage formula, may the variable be in any spot or any term. Once we get the terms in the percentage formula, we alter it so the variable is on the left-hand side and all the numerical on the right-hand side for easy calculation using simple mathematical algebra.