# 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(3464)   (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.