SOLUTION: Determine the equation of joint variation. Then solve for the missing value. x varies directly with y and z. x = 400 when y = 8 and z = 10. Find x when y = 10 and z = 12.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Determine the equation of joint variation. Then solve for the missing value. x varies directly with y and z. x = 400 when y = 8 and z = 10. Find x when y = 10 and z = 12.      Log On


   

Question 1064183: Determine the equation of joint variation. Then solve for the missing value.
x varies directly with y and z.
x = 400 when y = 8 and z = 10.
Find x when y = 10 and z = 12.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

"x varies directly with y and z" means that
x+=+k%2Ay%2Az
where k is some fixed number (yet to be determined)

We're given "x = 400 when y = 8 and z = 10" so let's plug those values in and solve for k
x+=+k%2Ay%2Az

400+=+k%2A8%2A10

400+=+k%2A80

400+=+80k

400%2F80+=+80k%2F80

5+=+k

k+=+5

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Since k+=+5 we can update the equation x+=+k%2Ay%2Az into x+=+5%2Ay%2Az

The equation of joint variation is x = 5*y*z

Now onto the question:
Find x when y = 10 and z = 12

So plug in y = 10 and z = 12 to get...

x+=+5%2Ay%2Az

x+=+5%2A10%2A12

x+=+50%2A12

x+=+600

So x = 600 when y = 10 and z = 12