Answer:
The Inverse variation says that:
[tex]y \propto \frac{1}{x}[/tex],
then the equation is of the form:
[tex]y = \frac{k}{x}[/tex] or [tex]xy = k[/tex]
Here, r represents the number of roses and w represents the number of weeds.
As per the statement:
The number of roses (r) in a garden increases when the number of weeds (w) decreases.
by definition of inverse variation:
[tex]rw = k[/tex] ....[1]
From the given table:
take any points
r = 20 and w = 10 then;
Substitute in [1] we have;
[tex](20)(10)= k[/tex]
Simplify:
k = 200
The equation becomes: [tex]rw = 200[/tex]
We have to find the number of roses when there are 5 weeds.
⇒w = 5
then;
[tex]r(5) = 200[/tex]
Divide both sides by 5 we get;
r = 40
Therefore, the number of roses are 40 when there are 5 weeds.
