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. We know that the average of these numbers is 36.

Step 2: Use the properties of consecutive even numbers Consecutive even numbers increase by 2 each time. For example, if the first number is x, the next four numbers would be x+2, x+4, x+6, and x+8.

Step 3: Use the information about the average The average of a set of numbers is the sum of the numbers divided by the quantity of numbers. In this case, we know that the average is 36 and there are 5 numbers. So, the sum of the numbers is 36*5 = 180.

Step 4: Set up an equation We know that the sum of the numbers is 180 and we know the form of each number. So, we can set up the following equation: x + (x+2) + (x+4) + (x+6) + (x+8) = 180

Step 5: Solve the equation Solving the equation gives x = 34. This is the smallest number in the set.

Step 6: Find the largest number The largest number in the set is x+8, which is 34+8 = 42. So, the largest number is 42.