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,
\[x\ multiplied\ by\ 4\ = \ x\ exceeds\ by\ 45\]
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,
\[3x = 45\]
\[x = \dfrac{45}{3}\]
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.