Question

The average of 5 positive numbers is 16. The highest of these numbers is

Answer 1

We don't know what these numbers are, so let's call them A, B, C, D, and E.

Since they are all positive integers, then they must be equal to or greater than 1

The average is calculated by adding A + B + C + D + E and dividing by 5, and we know that it should equal to 16. This gives us the following equation:

(A+B+C+D+E)/5 = 16

Since this is an equation, we can multiply both sides by the same number without affecting the equality. In this case, multiplying both sides by 5 gives us:

A+B+C+D+E = 16 * 5 = 80 (where A, B, C, D, E >= 1)

The only way for one of these number to have the largest possible value, is for all the other numbers to have the smallest possible value (which is 1)

So lets maximize A by making B, C, D, and E equal to 1

Now the equation can be rewritten as:

A + 1 + 1 + 1 + 1 = 850

Looking at this equation, it should be obvious that making B, C, D, and E greater than 1 would mean that A would have to be smaller in order for them all to still add up to 850

Performing addition gives us:

A + 4 = 80

A = 80 - 4

A = 76