Question

The variable z is directly proportional to x, and inversely proportional to y. When x is 4 and y is 10, z has the value 0.8. What is the value of z when x= 13, and y= 18

Answer 1

Answer:

13/9

Step-by-step explanation:

Directly proportional means it will be multiply to our constant k.

Inversely proportional means it will divide our k.

So we are given z is directly proportional to x and inversely proportional to y.

This means:

$z=k \cdot \frac{x}{y}$.

We are given (x=4,y=10,z=0.8).  We can use this to find k.  The k we will find using the point will work for any point (x,y,z) since k is a constant.  A constant means it is to remain the same no matter what.

$0.8=k \cdot \frac{4}{10}$

$0.8=k(.4)$

Divide both sides by .4:

$\frac{0.8}{0.4}=k$

$k=2$

The equation for any point (x,y,z) is therefore:

$z=2 \cdot \frac{x}{y}$.

We want to find z given x=13 and y=18.

$z=2 \cdot \frac{13}{18}$

$z=\frac{2 \cdot 13}{18}$

$z=\frac{13}{9}$