Question

The sum of three consecutive numbers is 99. Find the smallest number.

• A. 32
• B. 34
• C. 35
• D. 33

Answer 1

The correct option is A 32

Let the smallest number be $x$
As the numbers are consecutive terms,
$\to$ Next number to $x$ will be $x+1$
$\to$ Next number to $x+1$ will be $x+1+1=x+2$

The sum of three consecutive numbers = 99
$\Rightarrow$ Smallest number + Next number to $x$ + Next number to $(x+1)=99$

$\Rightarrow x+(x+1)+(x+2)=99$

Concept: Multiply the variable by number of times it occured.
$\Rightarrow (3\times x)+3=99$

Step 1: Subtract 3 from both sides of the equation to eliminate the constant on the left side of the equation.
$3x+3-3=99-33x=96$

Step 2: Now, Divide both sides by 3 to eliminate 3 on the left side of the equation.
$\frac{3x}{3}=\frac{96}{3}x=32$

Next number to x will be $x+1=32+1=33$
Next number to x + 1 will be $x+2=32+2=34$

Let's check it out:
The sum of three consecutive numbers = 99
32 + 33 + 34 = 99

Hence, The smallest number is $x$ which is 32.