Three consecutive integers add up to 51. What are these integers?

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13,14,15

16,17,18

19,20,21

22,23,24

answer is B.

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Detailed Solution

Given, three consecutive integers add up to 51.
Let the first integer be x,
Second integer be x+1,
Third integer will be x+1+1
=x+2
Sum of integers is 51.
Linear equation will be x+(x+1)+(x+2)=51
Simplifying the equation,

x + x + x + 1 + 2 = 51 ⇒ 3 x + 3 = 51 ⇒ 3 x = 51 − 3 ⇒ 3 x = 48

Divide both the sides by 3,
x=16
Substitute value of x, in first, second and third integer.
First integer is x=16.
Second integer is,
=x+1
=16+1
=17
Third integer is,
=x+2
=16+2
=18
Hence, the three consecutive integers are 16,17 and 18.
Correct option is 2.

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