If the average of five consecutive even numbers is 36, what is the largest of these numbers?

Step 1: Understand the problem The problem is asking for the largest number in a set of five consecutive even numbers, given that the average of these numbers is 36.

Step 2: Formulate a plan Since the numbers are consecutive even numbers, they can be represented as n, n+2, n+4, n+6, and n+8. The average of these numbers is the sum divided by the count, which is 5 in this case. So, we can set up the equation (n + n+2 + n+4 + n+6 + n+8) / 5 = 36.

Step 3: Solve the equation Solving the equation gives us the value of n. Once we have the value of n, we can find the largest number by adding 8 to n.

Step 4: Solve the problem First, simplify the equation: (5n + 20) / 5 = 36. This simplifies to n + 4 = 36. Solving for n gives n = 32. The largest number is then n + 8 = 32 + 8 = 40.

So, the largest number in the set is 40.