the average (arithmetic mean) of a and b is 6 and the average of a, b, c is 11. What is the value of c?

(a+b)/2 = 6

a+b = 12

(a+b+c)/3 = 11
a+b+c = 33
12+c = 33
c = 21

Well, if the average of a and b is 6, and the average of a, b, and c is 11, then we can safely assume that c must be on vacation somewhere tropical enjoying piña coladas and sunshine! But don't worry, c will eventually return with a value. Until then, let's hope a and b can handle being the average Joe's.

To find the value of c, we must first solve for the values of a and b.

We are given that the average of a and b is 6, so we can set up the equation:

(a + b) / 2 = 6

Next, we are given that the average of a, b, and c is 11, so we can set up the equation:

(a + b + c) / 3 = 11

To solve these equations, we need to isolate the variables.

First, let's solve the first equation for a + b:

a + b = 12

Now, let's solve the second equation for a + b + c:

a + b + c = 33

To find the value of c, we can subtract the equation a + b = 12 from the equation a + b + c = 33:

(a + b + c) - (a + b) = 33 - 12

c = 33 - 12

c = 21

Hence, the value of c is 21.

To solve this problem, we can use the formula for the arithmetic mean:

Average = (Sum of the numbers) / (Number of numbers)

Here, we know that the average of a and b is 6. So, we can set up the following equation:

(a + b) / 2 = 6

Multiplying both sides by 2 gives us:

a + b = 12 --- Equation 1

We also know that the average of a, b, and c is 11. Therefore, we can set up another equation:

(a + b + c) / 3 = 11

Multiplying both sides by 3 gives us:

a + b + c = 33 --- Equation 2

Now we have a system of two equations (Equation 1 and Equation 2) with two variables (a and b). We can solve for a and b using these equations, and then substitute their values into Equation 2 to find the value of c.

From Equation 1, we can express a in terms of b:

a = 12 - b

Substituting this expression for a into Equation 2:

(12 - b) + b + c = 33

Simplifying the equation:

12 + c = 33

Subtracting 12 from both sides gives us:

c = 33 - 12

Therefore, the value of c is 21.