The sum of three consecutive even integers is 90. What is the largest of these integers?
Understanding the Sum of Three Consecutive Even Integers: What Is the Largest?
When you encounter a problem like “The sum of three consecutive even integers is 90,” it’s more than just a math puzzle—it’s a gateway to understanding sequences, algebra, and logical reasoning. In this article, we’ll solve the equation step-by-step and reveal how to find the largest of these integers. Whether you're a student, a teacher, or someone curious about number patterns, this is a clear and practical guide.
What Are Consecutive Even Integers?
Consecutive even integers are numbers like 2, 4, 6 or 14, 16, 18 — each differing by exactly two. Because even numbers are always two units apart, finding three in sequence is straightforward: if the first is n, the next two are n+2 and n+4.
Setting Up the Equation
Let the first even integer be: n
Then the next two consecutive even integers are: n + 2 and n + 4
The sum of these three integers is given as 90: n + (n + 2) + (n + 4) = 90
Solving the Equation Step-by-Step
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Combine like terms: 3n + 6 = 90
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Subtract 6 from both sides: 3n = 84
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Divide both sides by 3: n = 28
Identifying All Three Integers
Now that we know n = 28, the three consecutive even integers are:
- First: 28
- Second: 30
- Third (largest): 32
Verifying the Solution
Let’s check: 28 + 30 + 32 = 90 ✅ All numbers are even and consecutive in sequence ✅ The largest is indeed 32 ✔️
Why This Matters: Real-World Applications
Understanding how to solve such equations helps in many practical scenarios—from organizing events in groups, managing schedules, or even designing algorithms in programming. Recognizing patterns in numbers builds critical thinking skills essential across STEM fields.
Final Answer
The largest of the three consecutive even integers that sum to 90 is 32.
Would you like to master similar math problems effortlessly? Explore step-by-step strategies and tips to strengthen your arithmetic and algebra skills today!
