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Question

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

A
32
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B
34
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C
35
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D
33
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Solution

## The correct option is A 32Let the smallest number be x As the numbers are consecutive terms, → Next number to x will be x+1 → Next number to x+1 will be x+1+1=x+2 The sum of three consecutive numbers = 99 ⇒ Smallest number + Next number to x + Next number to (x+1)=99 ⇒x+(x+1)+(x+2)=99 Concept: Multiply the variable by number of times it occured. ⇒(3×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=99−3 3x=96 Step 2: Now, Divide both sides by 3 to eliminate 3 on the left side of the equation. 3x3=963 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.

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