Inverse relationships

Question

suppose that y varies directly as x and inversely as z.  If y = 4 when x = 1/4 and z = 1/2, find y when x = 2 and z = 16.

Answer 1

Billy,

Your first statement tells us the following relationship:

 

y = kx/z      where k is a constant to be determined.

 

To find them, we plug in the values given.

 

4 = k(1/4)/(1/2)     first simplify this

 

4 = k(1/2)          solve for k

 

8 = k       Now we Know the relationship y = 8x/z

 

So for the final condition  y = 8(2)/16 = 1.