Question

A number when multiplied by \[5\] is increased by \[80\]. Find the number.

Answer 1

Hint: We use the concept of linear equations here to solve this problem. When two different mathematical expressions are expressed on either side of the ‘equal to’ or ‘ $ = $ ’ sign, it is said to be an equation. When such an equation is graphically represented, if the line in the graph is a straight line, the equation is one that is linear.

Complete step-by-step answer:
A statement is given in the question, describing the conditions of a particular number.
Let the unknown number be considered as $ x $ .
We can translate the given statement into a proper mathematical equation. Since we have only one unknown value here, we just need a linear equation in one variable. When only such a single variable exists, there can strictly be only one particular solution or value that satisfies the linear equation.
The given statement can be considered in two parts, in mathematical terms it is before and after the ‘equal to’ sign. In the statement, we consider the part before the word ‘is’ to be placed on the left hand side of the ‘ $ = $ ’ symbol and similarly the part of statement after ‘is’ is to be placed on the right side of that same ‘ $ = $ ’ symbol.
The first part says: “number multiplied by \[5\]”, this can be translated into mathematical terms as follows:
 $ (x) \times 5 $
The second part says: “number is increased by \[80\]”, this in mathematical terms will be:
 $ (x) + 80 $
Now let us put the ‘ $ = $ ’ between the two parts:
 $ \Rightarrow (x) \times 5 = (x) + 80 $
If we solve the equation and find the value of the variable $ x $ , we will have found the required number.
Let us proceed to solving the equation:
 $ \Rightarrow 5x = (x) + 80 $
Now bring all the terms containing the variable to one side, say left hand side:
 $ \Rightarrow 5x - x = 80 $
Now simplifying we get:
 $ \Rightarrow 4x = 80 $
 $ \therefore x = 20 $
Therefore the required number is the value of $ x $ , that is found to be $ 20 $ .
So, the correct answer is “20”.

Note: Here we had solved a linear equation using a manual method. But remember that there can be many different ways of solving a linear equation. We can use matrices to find the solution, we can use graphing methods and we can also use a substitution method. Sometimes when we have multiple equations we also use elimination methods.