Question

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

Answer 1

The Inverse variation says that:

`y \propto (1)/(x)`,

then the equation is of the form:

`y = (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.

Answer 2

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.