SOLUTION: The average of m numbers is a and the average of n numbers is b. If the average of all the (m+n) numbers is k, what is the value of m?

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Question 1183229: The average of m numbers is a and the average of n numbers is b. If the average of all the (m+n) numbers is k, what is the value of m?
Found 2 solutions by math_helper, ankor@dixie-net.com:
Answer by math_helper(2461) (Show Source):
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Sum of first group of numbers is am
Sum of 2nd group of numbers is bn

Average of (m+n) numbers is therefore: (am+bn)/(m+n) = k

Solving for m:

m = (kn-bn) / (a-k) ,

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
The average of m numbers is a and the average of n numbers is b.
If the average of all the (m+n) numbers is k, what is the value of m
:
the total in 1st group + the total in the 2nd group divided by (m+n) = k

ma + nb = k(m+n)
ma + nb - km + kn
ma - km = kn - nb
m(a-k) = n(k-b)
:
m =