The sum of three consecutive even integers is 90. What is the largest integer?
["The Sum of Three Consecutive Even Integers Is 90. What Is the Largest Integer?", "If you’ve ever encountered a problem involving three consecutive even integers, you might wonder how to quickly find their sum and determine the largest one. In this article, we’ll explore how to solve the equation where the sum of three consecutive even integers equals 90 — and identify the biggest of the three.", "---", "### Understanding Consecutive Even Integers", "Even integers are whole numbers divisible by 2, such as ..., -4, -2, 0, 2, 4, 6, … They increase by 2 each time. So, when we talk about three consecutive even integers, we’re referring to three numbers in a row like:", "- Let the first even integer be x\n- The next consecutive even integer is x + 2\n- The third is x + 4", "---", "### Setting Up the Equation", "The sum of these three integers is given as 90:", "[\nx + (x + 2) + (x + 4) = 90\n]", "Now simplify the left side:", "[\nx + x + 2 + x + 4 = 3x + 6\n]", "So:", "[\n3x + 6 = 90\n]", "---", "### Solving for x", "Subtract 6 from both sides:", "[\n3x = 84\n]", "Now divide by 3:", "[\nx = 28\n]", "---", "### Finding All Three Integers and the Largest", "Since x = 28, the three consecutive even integers are:", "- First: 28\n- Second: 30\n- Third: 32", "Their sum is:\n[\n28 + 30 + 32 = 90 \quad \ ext{(correct!)}\n]", "The largest integer among them is 32.", "---", "### Verifying the Solution", "Let’s double-check:\n28 + 30 = 58, and 58 + 32 = 90. ✅\nAll numbers are even and consecutive. ✅", "---", "### Why This Method Works", "Using consecutive even integers defined as x, x+2, x+4 allows us to combine the numbers algebraically. This simple setup reveals that the average of the three numbers equals the middle one, and since their sum is 90, the average is 30 — confirming the middle number is 30. Adding 2 and 4 around 30 gives the full set.", "---", "### Conclusion", "When the sum of three consecutive even integers is 90, solving the equation confirms that the largest integer is:", "32", "This straightforward approach helps quickly solve common math problems involving sequences and sums — ideal for students, educators, or anyone looking to strengthen their understanding of even numbers and algebraic reasoning.", "---", "Keywords: consecutive even integers sum to 90, largest even integer 90, how to find largest of three consecutive evens, solve even integer sum problem, math equation solution, even numbers algebra"]
