Question

The average (arithmetic mean) of four numbers is 4a + 16. When a fifth number is added, the average becomes 5a + 20. The fifth number is

A. a - 4
B. a + 4
C. 4a + 4
D. 4a + 16
E. 9a + 36

Answer 1

`9a+36`

Explanation:

The average (arithmetic mean) of four numbers is 4a + 16. When a fifth number is added, the average becomes 5a + 20.

The average (arithmetic mean) of four numbers is 4a + 16.

Sum of 4 numbers = 4 times the average

Sum of 4 numbers =
`4(4a+16)= 16a+64`

sum of 5 numbers = 5 times the average of 5 numbers

Sum of 5 numbers =
`5(5a+20)=25a+100`

fifth number = sum of 5 numbers minus the sum of 4 numbers

`fifth \ number = 25a+100-(16a+64)`

`25a+100-16a-64`

`9a+36`