The sum of three consecutive even integers is $72$. Find the integers

• A. $22,24,26$
• B. $20,22,30$
• C. $23,24,25$
• D. $18,24,30$

Answer: (A)

Verified step by step guidance

1. Let the three consecutive even integers be represented as \(x\), \(x + 2\), and \(x + 4\), where \(x\) is the smallest even integer.
2. Write an equation expressing the sum of these three integers: \(x + (x + 2) + (x + 4) = 72\).
3. Combine like terms on the left side of the equation: \(3x + 6 = 72\).
4. Isolate the variable term by subtracting 6 from both sides: \(3x = 72 - 6\).
5. Solve for \(x\) by dividing both sides by 3: \(x = \frac{72 - 6}{3}\), then find the three integers as \(x\), \(x + 2\), and \(x + 4\).