To solve this problem you must apply the proccedure shown below:
1. You have that [tex] y [/tex] varies inversely with [tex] x [/tex] and when [tex] x=13 [/tex] the value of [tex] y [/tex] is [tex] y=100 [/tex].
2. Therefore, you can write the following expression, where [tex] k [/tex] is the constant of proportionality:
[tex] y=\frac{k}{x} [/tex]
3. Solve for the constant of proportionality and substitute the values to calculate it:
[tex] k=yx\\ k=(100)(13=\\ k=1300 [/tex]
4. The equation is:
[tex] y=\frac{1300}{x} [/tex]
The answer is: [tex] k=1300\\ y=\frac{1300}{x} [/tex]
