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.

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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= 10.40476

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