The sum of three consecutive even integers is 114. define a variable for the smallest integer. define variables to represent the 2nd and 3rd integers. write an equation for the sum of the three consecutive even integers. solve the equation to find the three even integers.

36,38 and 40 are the three consecutive even integers

Step-by-step explanation:

As we Know that we have three consecutive even integers and even integers can be Obtained by adding or subtracting 2 from the given Number

Now According to the given condition we have three consecutive even integers

Let First even integer be x

Second even integer would be x + 2

Third even integer would be x + 2 + 2 = x + 4

Now According to the first condition

Sum of three integers = 114

so it would become

x + ( x + 2 ) + ( x + 4)=114  (i)

This would be the equation

Solving it

x + x + 2 + x + 4 = 114

3x + 6 =114

subtracting 6 from both sides

3x + 6 - 6 = 114 -6

3x = 108

Dividing both sides by 3

x = 108 /3

x = 36

Now second integer = x + 2                  and third integer = x + 4

Putting the value of x

Second integer = 36 + 2                               third integer = 36 +4

                           = 38                                                            = 40

So three consecutive even integers are 36,38 and 40

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