Question

A number when multiplied by $$4$$, exceeds itself by $$45$$. Find the number.

Answer 1

Hint: In this question, we need to find the unknown number. Let us consider the unknown number be $$x$$ and then proceed as the question says . Here the word exceeds is nothing but a number is added up. By forming an algebraic expression according to the question, we can find the unknown number.

Complete step-by-step solution:
Let the unknown number be $$x$$
Given,
$$xmultipliedby4=xexceedsby45$$
By forming the algebraic expression,
We get,
$$x\times 4=x+45$$
By simplifying,
We get,
$$4x=x+45$$
By moving the variables to one side,
We get,
$$4x–x=45$$
By subtracting,
We get,
$$3x=45$$
$$x={\displaystyle \frac{45}{3}}$$
By simplifying,
We get,
$$x=15$$
Thus we get the unknown number as $$15$$
We can also check whether our answer is correct or not.
We have already formed an algebraic expression according to the question.
That is
$$x\times 4=x+45$$
Here we can substitute the x value to check whether our answer is correct or not.
Here our $$x$$ is $$15$$
 $$15\times 4=15+45$$
By simplifying,
We get,
$$60=60$$
Thus $$L.H.S=R.H.S$$
From this we can conclude that our answer is absolutely correct.

Note: An algebraic expression is built up with integers, constants, variables and mathematical operations (addition, subtraction, multiplication, division etc… ) In mathematics, a symbol (letter) which doesn’t have a value is called a variable. Similarly which has a fixed value is called constant.