Question

A movie-theater employee notes an inverse relationship between the theater's popcorn sales and its nacho sales. On a given night, the theater makes $2,254 from popcorn sales and $1,628 from nacho sales. If on the next night the employees sell $2,024 of popcorn, how much is earned from nachos?

Answer 1

the employee earned $1813 from Nachos

Step-by-step explanation:

The theater's popcorn sales is inversely proportional to nacho sales

Let theater's popcorn = P

nacho sales = N

`P\text{ }\alpha\text{ }(1)/(N)`

Equating the relationship:

`\begin{gathered} P\text{ = k(}(1)/(N)) \\ P\text{ = }(k)/(N) \\ \text{where k = constant of proportionality} \end{gathered}`

when theater sales = $2,254

Nacho sales = $1,628

`\begin{gathered} 2254\text{ =}(k)/(1628) \\ k\text{ = 2254(1628)} \\ k\text{ = 3}669512 \end{gathered}`

The relationship becomes:

`P\text{ = }(3669512)/(N)`

When cost of the theater popcorn = $2,024

The cost from nachos = ?

We would use the relationship to get the above:

`\begin{gathered} 2024\text{ = }(3669512)/(N) \\ 2024N\text{ = 3669512}18 \\ N\text{ = }\frac{\text{3669512}}{2024} \\ N\text{ = }1813 \end{gathered}`

Hence, the employee earned $1813 from Nachos