Question

The sum of four numbers is 20 and their average is 5. When a fifth is added, the new average is 6. What is the fifth number?

Answer 1

10.

Explanation:

The average of the 5 numbers =

(20 + x) / 5 = 6 where x is the 5th number.

20 + x = 30

x = 10

The fifth number is 10.

Answer 2

10

Explanation:

We'll note the numbers as
`x_(n), x_(n+1) ...`

`x_1 + x_2 + x_3 + x_4 = 20\\Avg = 5\\(x_1 + x_2 + x_3 + x_4 + x_5 )/(5) = 6 = (20 + x_5)/(5)\\ 4 + (x_5)/(5) = 6\\\\frac{x_5}{5} = 2\\\x_5 = 10`