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