Question 1011683
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The sum of three numbers is 165. When the smallest number is multiplied by 7, the result is $n$. The value $n$ is obtained by subtracting 9 from the largest number. This number $n$ also results by adding 9 to the third number. What is the product of the three numbers?
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You use terms "smallest number", "largest number" and "third number". 
They are not the terms of one semantic row. Which is bad.


Nevertheless, I conclude the "third number" is the "medium/middle number".


If it is not so, then your formulation is simply provocation. 


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From the condition, this system of three equations for three unknowns arises

s + m + l = 165,   (1)
7s = l - 9,        (2)
l - 9 = m + 9.     (3).

where s is the smallest, l is the largest and m is the medium ("the third") number. 

Solve it, if you can. 

If not, then confirm that the "third number" is the medium.

Or re-edit and re-post your quest.
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