Question

The sum of three consecutive even integers is –78. What are the integers? Describe how you would use the strategy of writing an equation to solve the given problem.

Answer 1

The three consecutive even integers are: 2n, (2n+2) and (2n+4).
we can suggest this equation for solve this problem:

2n+(2n+2)+(2n+4)=-78

2n+2n+2n=-78-2-4
6n=-84
n=-84/6
n=-14

The three consecutive even integers are:
2n=2(-14)=-28
2n+2=2(-14)+2=-26
2n+4=2(-14)+4=-24

we check it out:
-28-26-24=-78

Answer: the equation will be : 2n+(2n+2)+(2n+4)=-78 and the three consecutive even integers are -28, -26 and -24. 

Answer 2

The given 3 consecutive integers if their sum is -78 will be -28, -26 and -24

Let the three consecutive even integers be x - 2, x and x+2

If the sum of three consecutive even integers is –78, hence;

x - 2 + x + x + 2 = -78

Collect the like terms

x + x + x - 2 + 2 = -78

3x = -78

x = -78/3

x = -26

Hence the given 3 consecutive integers will be -28, -26 and -24

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