Question

If 13 is added to one-half of a certain number, the result is \[37\] . the original number is equal to
A). \[24\]
B). \[40\]
C). \[48\]
D). \[61\]

Answer 1

Hint: To find the original number for the given condition, we need to subtract the number $13$ from $37$. Now given in question that the original number is halved. Hence it is doubled to the result. This gives the original number.

Complete step-by-step solution:
Let us consider the original number given in question as $x$ .
Initially the number is halved i.e., $\dfrac{x}{2}$
This number is added to $13$
$\Rightarrow \dfrac{x}{2}+13$
This result is equal to $37$ .
$\Rightarrow \dfrac{x}{2}+13=37$
Now to find $x$ solve the above equation with the help of basic mathematical operations.
Subtract both sides of the equation with $13$ .
$ \Rightarrow \dfrac{x}{2}+13=37 $
$ \Rightarrow \dfrac{x}{2}+13-13=37-13 $
$ \Rightarrow \dfrac{x}{2}=24 $
next multiply the above obtained equation with $2$
$ \Rightarrow \dfrac{x}{2}\times 2=24\times 2 $
$ \Rightarrow x=24\times 2 $
$ \Rightarrow x=48 $
Hence the original number given in question is $48$ which is given by option (C).

Additional information: Linear equations are those whose equations have the degree of one. They are called linear equations because when a graph is drawn it will be a straight line. The basic mathematical operations we use in this question are addition, subtraction, multiplication and division.

Note: For linear equations with one variable there exists only one solution. For linear equations in a single variable the standard equation can be given as $ax+b=c$. For solving linear equations in a single equation, we require only one equation, for two variables two equations are required. However, the graph for a single variable equation will be a point on the graph which represents the value of the single variable.