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The sum of three consecutive integers is 45. Find the integers.

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14, 15, 16

12, 13, 14

15, 16, 17

16, 17, 18

answer is A.

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Detailed Solution

Concept- In this question, first of all assume three consecutive integers as

x, (x + 1)

and

(x + 2)

. Now, add them and equate to forty five and find the value of x from the equation, and from x, find the 3 consecutive integers.
Value of the first integer =

x

Let this equation as equation (1)
Value of the second integer =

x + 1

Let this equation as equation (2)
Value of the third integer =

x + 2

Let this equation as equation (3)
Given that the sum of three subsequent integers is 45.
So, we get,

(First Integer) + (second Integer) + (Third Integer) = 45

By substituting the value of the first, second and third integers from equation (1) , (2) and (3)

3 x + 3 = 45

3 x = 45 - 3

3 x = 42

x = \frac{42}{3}

x = 14

So, we get the first integer =

x = 14

Value of the second integer =

x + 1 = 15

Value of the third integer =

x + 2 = 16

Hence, the correct option is 1) 14, 15, 16

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