Question

A number when added to its half gives 72. Find the number.

Answer 1

Hint: To find the number, we will assume a variable for that number, say x. Then, according to the given condition, we will form an equation by adding the assumed number x and $\dfrac{\text{x}}{\text{2}}$ and equating it to 72. Then we will solve this equation for the value of x.

Complete step-by-step answer:
Let the required number be x.
According to the given condition, when we find the sum of the number and the half of that number, we get 72.
Half of any number is obtained by dividing the number by 2. For example, half of 4 can be obtained by dividing by 2, like $\dfrac{4}{2}$ = 2. Similarly, the assumed number with us is x. Thus, the half of the number will be $\dfrac{\text{x}}{2}$.
Therefore x +$\dfrac{\text{x}}{\text{2}}$ = 72.
Now, we make the denominator the same in the left-hand side.
$\Rightarrow \dfrac{\text{2x+x}}{\text{2}}$ = 72
Then, we will add 2x and x.
\[\Rightarrow \dfrac{\text{3x}}{\text{2}}\] = 72
We will now cross multiply 2.
\[\Rightarrow \]3x = 72 (2)
\[\Rightarrow \]3x = 144
Now, we divide 144 by 3.
\[\Rightarrow \]x = $\dfrac{144}{3}$ = 48
Therefore, the number is 48.

Note: We can verify the obtained solution. To verify, we will add the obtained solution 48 and half of 48. Half of 48 will be $\dfrac{48}{2}$ = 24. So, 48 + 24 = 72. This proves that the answer we got verifies with the conditions given in the question. Hence, our solution is correct. Students are advised to be careful while forming the equation as the answer depends on the equation we form.