SOLUTION: Multiple Choice: if one half the average of 3 numbers a, b and c is equal to twice the average of a and b, then c=____. a) 2(a+b) b) 3(a+b) c) 4(a+b) d) 5(a+b)

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Question 1059597: Multiple Choice: if one half the average of 3 numbers a, b and c is equal to twice the average of a and b, then c=____.
a) 2(a+b) b) 3(a+b) c) 4(a+b) d) 5(a+b)
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The average of all 3 numbers is %28a%2Bb%2Bc%29%2F3 .
The average of a and b is %28a%2Bb%29%2F2 .
The problem says that
%281%2F2%29%2A%28%28a%2Bb%2Bc%29%2F3%29=2%2A%28%28a%2Bb%29%2F2%29
which simplifies to
%28a%2Bb%2Bc%29%2F6=a%2Bb .
Multiplying both sides of the equal sign times 6 . we get the equivalent equation
a%2Bb%2Bc=6%28a%2Bb%29
Subtracting %28a%2Bb%29 from both sides of the equal sign we get
c=6%28a%2Bb%29-%28a%2Bb%29 , which simplifies to
highlight%28c=5%28a%2Bb%29%29 .