Question

Half of a number is added to \[24\] then the sum is \[66\]. The number is
A) 84
B) 88
C) 74
D) 98

Answer 1

Hint:
Here, we have to find the number. We will assume the number to be some variable and then divide it by 2 to get the half of the number. We will then frame a linear equation based on the given information. We will then solve the equation to get the required number.

Complete step by step solution:
Let \[x\] be a number, so half the number is \[\dfrac{x}{2}\]
We are given that half a number is added to \[24\] then the sum is. Therefore, we get
\[\dfrac{x}{2} + 24 = 66\]
Subtracting 24 from both the sides, we get
\[ \Rightarrow \dfrac{x}{2} = 66 - 24\]
\[ \Rightarrow \dfrac{x}{2} = 42\]
Multiplying by 2 on both the sides, we get
\[ \Rightarrow \dfrac{x}{2} \times 2 = 42 \times 2\]
\[ \Rightarrow x = 84\]
Therefore, the number is \[84\].

Thus, option (A) is the correct answer.

Note:
We know that a linear equation is defined as an equation with the highest degree as 1 and has only one solution. Linear equations are a combination of constants and variables. Similarly, we have linear equations in two variables, linear equations in three variables and so on. We can solve the linear equations in two variables using elimination and substitution methods and the linear equations in three variables by using the matrix method.
Here, we can make a mistake by adding the number to 24 instead of adding half of the number to it. We can also make another mistake by adding the number and 24 and finding its half. These two mistakes will give us the wrong answer.