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

Answer:

$9a+36$

Step-by-step 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

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

$25a+100-16a-64$

$9a+36$