Find three consecutive positive even integers such that four times the first decreased by the second is 12 more than twice the third.

n-2, n, n+2

4(n-2) - n = 12 + 2(n+2)

4 n - 8 - n - 12 - 2n - 4 = 0

n - 24 = 0

n = 24

22 , 24, 26

Why did the even integers want to find each other? Because they wanted to have an "even" better time when hanging out!

Let's call the first positive even integer "x." The next consecutive positive even integer would then be "x + 2," and the one after that would be "x + 4."

According to the problem, we have the equation: 4x - (x + 2) = 2(x + 4) + 12.

Simplifying that gives us: 4x - x - 2 = 2x + 8 + 12.

Now let's solve it like a clown solving a puzzle!

Combining like terms, we have: 3x - 2 = 2x + 20.

Subtracting 2x from both sides gives us: x - 2 = 20.

Adding 2 to both sides, we get: x = 22.

So, our first positive even integer is 22.

The next consecutive positive even integer is 22 + 2 = 24.

And the one after that is 24 + 2 = 26.

Therefore, our three consecutive positive even integers are 22, 24, and 26.

Let's assume the first positive even integer as "x", then the next two consecutive positive even integers would be "x+2" and "x+4".

According to the given statement, four times the first decreased by the second is 12 more than twice the third. We can represent this as an equation:

4x - (x+2) = 2(x+4) + 12

Simplifying the equation:

4x - x - 2 = 2x + 8 + 12

Combining like terms:

3x - 2 = 2x + 20

Moving all variables to one side:

3x - 2x = 20 + 2

x = 22

So, the first positive even integer is 22. The next two consecutive positive even integers would be 24 and 26, respectively.

Therefore, the three consecutive positive even integers are 22, 24, and 26.

To solve this problem, let's represent the three consecutive positive even integers as x, x+2, and x+4.

According to the given problem, "four times the first decreased by the second is 12 more than twice the third" can be translated into an equation:

4x - (x+2) = 2(x+4) + 12

Let's solve this equation to find the value of x:

4x - x - 2 = 2x + 8 + 12

Combine like terms:

3x - 2 = 2x + 20

Subtract 2x from both sides:

x - 2 = 20

Add 2 to both sides to isolate x:

x = 22

Now, substitute the value of x back into the expression for the three consecutive positive even integers:

x = 22
x+2 = 24
x+4 = 26

Therefore, the three consecutive positive even integers are 22, 24, and 26.