Question

Three times a number equal to \[40\] more than five times the number . What is the number?

Answer 1

Hint: In this question, given that Three times a number equal to \[40\] more than five times the number. We need to find the unknown number. Let us assume the unknown number by a variable and we need to proceed and form an algebraic expression as per the question says. An algebraic expression is nothing but it 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.At first, we need to form the expression according to the question, and on simplifying we can find the unknown number.

Complete step-by-step solution:
Given, Three times a number equal to \[40\] more than five times the number .
Let us assume the unknown number be \[x\].
Now we can form the expression as per the question.
\[\Rightarrow \ 3 \times x = 40 + 5x\]
On moving the variable terms to one side ,
\[\Rightarrow \ 3x – 5x = 40\]
On simplifying,
We get,
\[- 2x = 40\]
\[\Rightarrow \ x = - \dfrac{40}{2}\]
On further simplifying,
We get,
\[\Rightarrow \ x = - 20\]
Thus we get the unknown number as \[- 20\] .
Final answer :
The number is \[- 20\].

Note: Mathematically, In some cases if we have to find \[2\] unknown variables, we have to form \[2\] linear equations with \[2\] variables. Similarly if we have \[3\] unknown variables, we have to form \[3\] linear equations with \[3\] variables. We can also check whether our answer is correct or not by substituting the number in the expression formed as per the question says. If both the left side and right side of the expression carries the same number, then our answer is absolutely correct.