z varies directly as x and inversely as y. If z=159 when x=8 and y=6, find z if x=5 and y=8.

Answer 1

Hello!

Try this,

Direct variation means as x gets bigger, y gets bigger (or both smaller).

The equation for direct variation is y = kx (where k is a constant of variation).

Inverse variation means as x gets bigger, y gets smaller (or vice versa).

The equation for inverse variation is yx = k.

Let's solve both of these equations for k, because we'll need that value to answer your question.

Direct variation ---- y = kx divide both sides by x, and put k on the other side

k = y

x

Inverse variation ---- yx = k already solved for k!

So to figure out the relationship between direct and inverse, and what happens to these numbers when this happens, we look at the equation. When we do direct, we are dividing. When we do inverse, we are multiplying.

Let's apply that to the problem. "z varies directly as x" so we need to divide. z / x

"z varies inversely as y", so we need to multiply. or zy. Combining these two we get a value for k

k = z y

x

Now, plug in the values you have of z, y and x to solve for k. Then use this equation again, plugging in x and y, then solve for z!

If you have any follow up questions just let me know. Good luck!

Answer 2