The sum of three consecutive even numbers is 90. Find the largest of these numbers. - Coaching Toolbox
The Sum of Three Consecutive Even Numbers Is 90: How to Find the Largest Number Simply
The Sum of Three Consecutive Even Numbers Is 90: How to Find the Largest Number Simply
Are you curious about how to quickly determine the sum of three consecutive even numbers when you already know their total? Discover an easy method to solve this classic math puzzle—perfect for students, teachers, and anyone interested in numbers.
In this article, we’ll explore how to find the largest of three consecutive even numbers whose total is 90, using simple algebra and logic. We’ll also explain why this approach works and how to apply it in real-life math problems.
Understanding the Context
What Are Consecutive Even Numbers?
Consecutive even numbers are even numbers that follow each other in sequence without gaps. For example: 2, 4, 6 or 10, 12, 14.
An important rule: Every set of three consecutive even numbers can be written as:
n, n + 2, n + 4,
where n is the smallest even number.
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Key Insights
Given: The Sum Equals 90
We’re told:
n + (n + 2) + (n + 4) = 90
Let’s simplify this step-by-step:
-
Add the expressions:
n + n + 2 + n + 4 = 90
→ 3n + 6 = 90 -
Solve for n:
3n = 90 – 6
3n = 84
n = 84 ÷ 3
n = 28
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So the three numbers are:
28, 30, and 32
Find the Largest Number
From the calculation above, the largest of the three consecutive even numbers is:
n + 4 = 28 + 4 = 32
Quick Verification
28 + 30 + 32 = 90 ✓
The largest number is indeed 32
A Faster Way to Solve Any Such Problem
Since three consecutive even numbers follow a simple arithmetic sequence, once you use the formula for the sum:
Sum = 3n + 6,
you can solve for n, then compute the largest number as:
Largest number = n + 4 = (90 – 6)/3 + 4 = 28 + 4 = 32
