SOLUTION: The average (arithmetic mean) of a and b is 10, whereas the average of b and 10 is c/2. What is the average of a and c?

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Question 258316: The average (arithmetic mean) of a and b is 10, whereas the average of b and 10 is c/2. What is the average of a and c?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
(a+b)/2 = 10 (first equation)

(b+10)/2 = (c/2) (second equation)

first equation states that the average of a and b is 10.

second equation states that the average of b and 10 is c/2

question is what is the average of a and c.

take the second equation and solve for b.

second equation is:

(b+10)/2 = c/2

multiply both sides of this equation by 2 to get:

b + 10 = c

subtract 10 from both sides of this equation to get:

b = c - 10

substitute for b in the first equation.

first equation is:

(a+b)/2 = 10

multiply both sides of this equation by 2 to get:

a + b = 20

subsstitute (c-10) for b to get:

a + c - 10 = 20

add 10 to both sides of this equation to get:

a + c = 30

divide both sides of this equation by 2 to get:

(a+c)/2 = 15

average of (a+c) is equal to 15.