The sum of three consecutive even numbers is 20 more than their average. Find the largest number.

Sure, let's solve this step by step:

Step 1: Let's denote the three consecutive even numbers as x, x+2, and x+4.

Step 2: The sum of these numbers is x + (x+2) + (x+4) = 3x + 6.

Step 3: The average of these numbers is (x + (x+2) + (x+4))/3 = x + 2.

Step 4: According to the problem, the sum is 20 more than the average. So, we can set up the following equation: 3x + 6 = x + 2 + 20.

Step 5: Simplify the equation to 3x + 6 = x + 22.

Step 6: Subtract x from both sides to get 2x + 6 = 22.

Step 7: Subtract 6 from both sides to get 2x = 16.

Step 8: Divide both sides by 2 to get x = 8.

Step 9: So, the three consecutive even numbers are 8, 10, and 12. The largest number is 12.