Question

there are 3 consecutive even integers that add up to 186. which integers are they?

Explanation:

Step1: Define the variables

Let the first even integer be \( x \). Then the next consecutive even integer is \( x + 2 \), and the third is \( x + 4 \).

Step2: Set up the equation

The sum of the three integers is 186, so we have the equation:

$$ x+(x + 2)+(x + 4)=186 $$

Step3: Simplify the equation

Combine like terms:

$$ 3x+6 = 186 $$

Step4: Solve for \( x \)

Subtract 6 from both sides:

$$ 3x=186 - 6=180 $$

Divide both sides by 3:

$$ x=\frac{180}{3}=60 $$

Step5: Find the other integers

The first integer is \( x = 60 \). The second integer is \( x + 2=60 + 2 = 62 \). The third integer is \( x + 4=60 + 4 = 64 \).

Answer:

60, 62, 64