The sum of three consecutive even integers is -114. what is the least of these numbers?

The sum of three consecutive even integers is -114. what is the least of these numbers? a. 40 b. -36 c. -40 d. -44

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  1. Let the integers be;
    x, x+2, x+4
    The sum is;
    x+x+2+x+4=-114
    3x+6=-114
    3x=-114-6
    3x=-120
    x=-40
    The least integer is thus -40

  2. 40 is the largest number !

    36 , 38 & 40 are the consecutive numbers having sum of 114 !

    Step-by-step explanation:

    • A consecutive numbers means number are in a sequence and are one after the another !

    • A consecutive even numbers differ by 2 because all even numbers are divisible by 2 !

    • If the number is divisible by x we must had taken number as n , ( n + x ) ,

    ( n + 2x )

    Let the consecutive even numbers be n ( n + 2 ) and ( n + 4 )

    Given :- Sum of the numbers is 114

    n + n + 2 + n + 4 = 114

    3n + 6 = 114

    3n = 114 - 6

    3n = 108

    n = 108/3

    n = 36

    So, the Consecutive even numbers are :-

    n = 36

    n + 2 = 36 + 2 = 38

    n + 4 = 36 + 4 = 40

    So, the Largest number is 40 !!

    • Verification :-

    36 + 38 + 40 = 114

    Hence, it satisfies the given condition !

    so, verified !

  3. 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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