If a+b+c=8, b+c=9, c+a=11 then what is the average of a, b and c.

First, we solve for all the variables. We use the system of equations. I will be making the equations b+c=9 and c+a=11 to have b=? and a=? and plug it in to the overall equation.

b+c=9

b=9-c

c+a=11

a=11-c

a+b+c=8 ← Plug in the above equations for their corresponding variable.

(11-c) + (9-c) + c=8 ← Remove parentheses

11-c+9-c+c=8 ← Combine like terms

20-c = 8

20 = 8 + c

20 - 8 = c

12 = c

Next, we plug c in to the other two equations to find a and b:

b + c=9

b+12=9

b=-3

c+a=11

12+a=11

a = - 1

Then, we have to find the average. There are three numbers, so we add up a, b, and c and we divide by 3.

(12 + - 3 + - 1) / 3 = (12-3-1) / 3 = 8/3 is the average