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 first even integer be represented by \(x\). Since the integers are consecutive even numbers, the next two integers can be expressed as \(x + 2\) and \(x + 4\).
2. Write an equation representing the sum of the three consecutive even 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 \(x + 4\).