Question

a birthday party at the trampoline park costs $225 to rent a party room, plus $15 per guest. the number of guests, $n$, as a function of cost, $c$ is given by the equation $n = \frac{c-225}{15}$.
a. how many guests attended if the party cost $585?
b. find the inverse.
d. what information does the inverse give you?

Explanation:

Step1: Substitute $C=585$ into formula

$n = \frac{585-225}{15}$

Step2: Calculate numerator first

$585-225=360$

Step3: Divide to find $n$

$n = \frac{360}{15}=24$
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Step4: Swap $n$ and $C$ for inverse

$n = \frac{C-225}{15}$ becomes $C = \frac{n-225}{15}$

Step5: Solve for new $C$

Multiply both sides by 15: $15n = C - 225$
Rearrange to isolate $C$: $C=15n+225$
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Step6: Interpret inverse function

The original function gives guests from cost; the inverse reverses this relationship.

Answer:

a. 24 guests
b. $C=15n+225$
d. The inverse function calculates the total cost of the party based on the number of guests attending.