Someone please help with solving this.

Question

The variable Z is directly proportional to X, and inversely proportional to Y. When X is 6 and Y is 3, Z has the value 6.

What is the value of Z when X = 10, and Y = 8

Answer 1

The problem initially tells you that Z is both directly proportional to X and inversely proportional to Y.  Therefore the equation we have looks something like

 

Z = w (X/Y)     where w is some constant we don't know.  With the first batch of information they give us, (X=6, Y=3. and Z=6 all at the same time), we can find whatever w is.

 

Z = w (X/Y)

6 = w (6/3)

w = 3

 

Therefore, our equation is actually Z = 3 (X/Y).  If they give us X and Y we can definitely find Z now.

 

Z = 3 (X/Y)

Z = 3 (10/8)

Z = 30/8

Z = 15/4 = 3.75

 

Hope that helps.  Let me know if you have any questions.

John

Answer 2

Since Z is a function of both X and Y, Z = aX/Y where a is a constant.  When X = 6 and Y = 3, Z = 6 or 6=a(6)/3.  a must equal 3, so Z = 3(X)/Y.  Now use X = 10 and Y = 8 to get Z.  Z = 3(10)/8 = 30/8 = 3.75 .