Question

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

`Z=2.99999999999995`

Explanation:

We can write the proportionality equation as:

`Z=k(X)/(Y)`

Note: Directly proportional goes top and top, multiplied. And inversely proportional goes top bottom, divided. Also, k is the proportionality constant.

When X is 3, Y is 19, Z is 0.94736842105263. Plugging these, we figure out k:

`Z=(kX)/(Y)\\0.94736842105263=(k(3))/(19)\\k=(0.94736842105263*19)/(3)\\k=5.99999999999999`

Now we put X = 13 and Y = 26 and k = 5.99999999999999, to find Z:

`Z=(kX)/(Y)\\Z=((5.99999999999999)(13))/(26)\\Z=2.99999999999995`