Question

The average (arithmetic mean) of a - 5 and a is x, and the average of a and a + 9 is y. What is the average of x and y?

a + 1
B) a +2
C) 2a + 1
D) 2a + 2

Answer 1

The answer is "Option A"

Explanation:

Given:

`\to ((a-5)+a)/(2)=x.....(a)\\\\\to (a+(a+9))/(2)=y.....(b)\\\\`

solve the above equation:

`\to \bold{((a-5)+a)/(2)=x}\\\\\to (a-5+a)/(2)=x\\\\\to (2a-5)/(2)=x\\\\\to \bold{(a+(a+9))/(2)=y}\\\\\to (a+a+9)/(2)=y\\\\\to (2a+9)/(2)=y\\\\`

add both value (x and y):

`\to \bold{x+y}\\\\\to (2a-5)/(2)+(2a+9)/(2)\\\\\to (2a-5+2a+9)/(2)\\\\\to (4a+4)/(2)\\\\\to (2(2a+2))/(2)\\\\\to (2a+2)\\`

average of x and y:

`\to (x+y)/(2)\\\\\therefore \bold{x+y= 2a+2}\\\\\to (2(a+1))/(2)\\\\\to \boxed{(a+1)}\\`