MHB Average of 2 Numbers: Find Equation Solution

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To find the average of two numbers when the average of 11 numbers is 14 and the average of 9 of those numbers is 9, the equation used is (81 + a + b) / 11 = 14. This leads to the conclusion that a + b equals 154. Dividing 154 by 2 gives the average of the two unknown numbers as 36.5. The discussion highlights the importance of setting up the correct equation to solve the problem efficiently. The solution demonstrates how to derive the average without resorting to trial and error.
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If average of 11 numbers is 14 and average of the 9 of those numbers is 9, what is the average of the other 2 numbers?

Answer 36.5

9x9 = 81 - how do I write equation to figure out other 2 numbers without trial and error?
 
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Hi alextrainer and welcome to MHB! :D

$$\frac{81+a+b}{11}=14$$

Can you continue with that?
 
Thanks, I got it

a plus b = 154

154/2 = answer

thanks for the equation
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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