Question

the smallest of three consecutive even numbers is 74 less than the sum of the three numbers. write and solve an equation to find the three numbers.

Explanation:

Step1: Define the even numbers

Let the smallest consecutive even number be $x$. The next two are $x+2$ and $x+4$.

Step2: Set up the equation

Smallest = Sum - 74
$x = (x + (x+2) + (x+4)) - 74$

Step3: Simplify the sum

$x = (3x + 6) - 74$
$x = 3x - 68$

Step4: Solve for $x$

$x - 3x = -68$
$-2x = -68$
$x = \frac{-68}{-2} = 34$

Step5: Find the other numbers

Second number: $34+2=36$
Third number: $34+4=38$

Answer:

The three consecutive even numbers are 34, 36, and 38.