The sum of three numbers $x$ ,$y$, $z$ is 165. When the smallest number $x$ is multiplied by 7, the result is $n$. The value $n$ is obtained by subtracting 9 from the largest number $y$. This number $n$ also results by adding 9 to the third number $z$. What is the product of the three numbers? Just take the $ out

You're given

x + y + z = 165

7x = n

n = y - 9

n = 9 + z

and you want to find xyz.

Solve the last three equations for x, y, and z :

7x = n   →   x = n/7

n = y - 9   →   y = n + 9

n = 9 + z   →   z = n - 9

Substitute x, y, and z into the first equation and solve for n :

n/7 + (n + 9) + (n - 9) = 165

n/7 + 2n = 165

n + 14n = 1155

15n = 1155

n = 77

Now solve for x, y, and z :

x = 77/7 = 11

y = 77 + 9 = 86

z = 77 - 9 = 68

Then the product is

xyz = 11 • 86 • 68 = 64,328

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