Question

Half of a number is added to 18, then the sum is 46. The number is ______.
A,92
B.56
C.65
D.0

Answer 1

Hint: To find the number, we have to assume the number to be x. Then we form an equation with x according to the given question. On solving the equation, we can find the value of x. The equation is solved by eliminating all terms from the left hand side except x.

Complete step-by-step answer:
Let the number be x.
Half of the number is \[\dfrac{1}{2}x\]
As per question, when half of a number is added to 18, the sum is 46. Therefore, the equation can be written as:
\[\dfrac{1}{2}x+18=46\]
The equation is solved as:
\[\dfrac{1}{2}x+18=46\]
\[ \dfrac{1}{2}x=46-18  \]
\[ \dfrac{1}{2}x=28 \]
\[ x=28\times 2 \]
\[ x=56 \]
Therefore, the number is 56.
So, the correct answer is “Option B”.

Note: Before cross multiplication of 2, 18 should be transferred to the other side. On transferring 18, its sign changes. Only when the numbers are subtracted, can we cross multiply 2. To check the solution, we can substitute the value of x in the original equation. If the values on both sides of the equation are equal, the value of x is correct. On substituting the value of x in the original equation we get,
\[ \dfrac{1}{2}x+18=46 \]
\[ \dfrac{1}{2}\times 56+18=46 \]
\[28+18=46 \]
\[ 46=46 \]
Since, LHS = RHS, the value of x is correct.
It should also be kept in mind that before all terms except x is eliminated from the left hand side, we cannot write the final value of x.