what is the value of z when x=23, and y=14

label Algebra
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the variable z is directly proportional to x, and inversely proportional to y. when x is 15 and y is 19, z has the value 5. 

Aug 7th, 2015

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x      y      z

15    19   5

When it comes to direct or inverse proportion there is a constant of proportion...

If x varies directly (or is directly proportional) with y then x = ky

If x varies inversely (or is directly proportional) with y then x = k/y

For this problem we have z directly proportional to x and inversely proportional to y

so:

z = kx/y

We are given initial values of x, y, z from which we can find the value of k

5= 15k/19

Multiply by 19 both sides

5 * 19=15k

k=95/15

k=6.333

Now we use  z = kx/y  with the known value of k and those given

z=6.333(23/14)

z= 10.40476 


Please let me know if you need any clarification. I'm always happy to answer your questions.
Aug 7th, 2015

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