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The number of roses (r) in a garden increases when the number of weeds (w) decreases. Write the correct equation for this scenario, and solve for the number of roses when there are 5 weeds.



Weeds Roses

10 20

20 10

Verified Answer :

meerkat18

Number of roses (r) in a garden increases when the number of weeds (w) decreases, this supports an inverse relationship between the two variables. 
The formula is then therefore, r = k/w
Solve for constant first.
r = k/w
20 = k/10
200 = k

r=200/5
r=40 roses
40 roses when there are 5 weeds.

Answer:

The Inverse variation says that:

\(y \propto \frac{1}{x}\),

then the equation is of the form:

\(y = \frac{k}{x}\) or \(xy = k\)

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:

\(rw = k\)          ....[1]

From the given table:

take any points

r = 20 and w = 10 then;

Substitute in [1] we have;

\((20)(10)= k\)  

Simplify:

k = 200

The equation becomes: \(rw = 200\)  

We have to find the number of roses when there are 5 weeds.

⇒w = 5

then;

\(r(5) = 200\)  

Divide both sides by 5 we get;

r = 40

Therefore, the number of roses are 40 when there are 5 weeds.

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