The sum of three consecutive even integers is 186. What is the value of the largest integer? - RTA

Understanding the Context

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How Does the Sum of Three Consecutive Even Integers Work?

Key Insights

To solve the sum of three consecutive even integers equaling 186, begin by recognizing that even numbers follow a precise pattern. Let the smallest integer be ( x )—an even number. The next two are ( x+2 ) and ( x+4 ). Adding them:

[ x + (x + 2) + (x + 4) = 186 ]

Combine like terms:

[ 3x + 6 = 186 ]

Subtract 6 from both sides:

Final Thoughts

[ 3x = 180 ]

Divide by 3:

[ x = 60 ]

The integers are 60, 62, and 64. Adding them:

[ 60 + 62 + 64 = 186 ]

The largest integer is 64—an even result reflecting the consistent spacing of consecutive evens. This method works reliably because even numbers maintain consistent increments, simplifying sum calculations.