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

Question

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

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Kim Cúc 4 years 2021-09-01T23:43:41+00:00 1 Answers 62 views 0

Answers ( )

  1. danthu
    0
    2021-09-01T23:45:15+00:00
    Reply

    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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