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The average of 10 numbers is 10. If a number is excluded from this set, then the new average becomes 9.

What is the value of the number that was excluded?

 Jun 23, 2020
 #1
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The sum of the numbers is 10x10=100. When we exclude a number x from this set, our new average is \(\frac{100-x}{9}\). We are told this equals 9. So our equation is \(\frac{100-x}{9}=9\).

Solve for x and you have your answer. 

 Jun 23, 2020
 #2
avatar+133 
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If the average of 10 numbers is 10, the sum of the numbers is \(10*10 \) or 100. If we remove a number, we get the following equation:

 

                                                                                                          \(\frac{100-x}{9} = 9\)

Now, we solve for \(x\):

 

\(\frac{100-x}{9} = 9\)

 \(900 - 9x = 81\)

 

We divide one side by 9 which results to:

 

\(100 - x = 81 \)

 

\(100 - 81 = 19 \)

 

We get the final result which is \(19=x\).

 Jun 23, 2020

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