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 piƱa 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.