Question

1. the cost that a carpet cleaning company charges is directly proportional to the number of rooms cleaned. the cost is $27 for each room. (a) (4 points) write a direct variation equation to represent the cost (b) (4 points) how many rooms can a hotel pay the company to clean for $256.50? write and solve an equation. you must show all your work to receive all credit.

Explanation:

Step1: Define variables for direct variation

Let $C$ = total cost, $r$ = number of rooms. Direct variation equation form: $C = kr$, where $k$ is the constant of proportionality.

Step2: Substitute given $k$ value

Given $k = 27$ (cost per room), so:
$C = 27r$
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Step3: Set up equation for part (b)

Substitute $C = 256.50$ into the variation equation:
$256.50 = 27r$

Step4: Solve for $r$

Divide both sides by 27:
$r = \frac{256.50}{27}$
$r = 9.5$

Answer:

(a) $C = 27r$
(b) 9.5 rooms