SOLUTION: Please help me solve for x, y, and z. x/2 + y/5 + z/3= 17 x/5 + y/2 + z/5= 32 x + y/3 + z/2= 30

Question 76702: Please help me solve for x, y, and z.
x/2 + y/5 + z/3= 17
x/5 + y/2 + z/5= 32
x + y/3 + z/2= 30
Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!


x/2 + y/5 + z/3 = 17
x/5 + y/2 + z/5 = 32
  x + y/3 + z/2 = 30

Multiply the first equation through by LCD 30.

30(x/2 + y/5 + z/3) = 30(17)
     15x + 6y + 10z = 510

Multiply the second equation through by LCD 10.

 10(x/5 + y/2 + z/5) = 10(32)
        2x + 5y + 2z = 320

Multiply the third equation through by LCD 6.

   6(x + y/3 + z/2) = 6(30)
       6x + 2y + 3z = 180

Now the system is easy to solve because it has
only whole numbers and no fractions:

       15x + 6y + 10z = 510
        2x + 5y +  2z = 320
        6x + 2y +  3z = 180

Can you solve it?  If not post again asking how.

Answer: (x, y, z) = (10, 60, 0)

Edwin

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