Question Below!

Question

Can someone help me solve this with the steps?

 

The variable Z is directly proportional to X, and inversely proportional to Y. When X is 3 and Y is 19, Z has the value 0.94736842105263.

What is the value of Z when X = 13, and Y = 26

Answer 1

When Z is directly proportional to X, that means that, for some number m, Z = mX.

 

Let's solve for m, knowing that when X = 3, Z = 0.94736842105263:

 

Z = mX

0.94736842105263 = m(3)

0.315789474 = m

 

So, when X = 13:

 

Z = mX

Z = 0.315789474(13)

Z = 0.315789474

 

 

 

When Z is inversely proportional to Y, then, for some number n, Z = n/Y.

 

Let's solve for n, knowing that when Y = 19, Z = 0.94736842105263:

 

Z = n/Y

0.94736842105263 = n/19

18 = n

 

So, when Y = 26:

 

Z = n/Y

Z = 18/26

Z = 0.692307692