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

Explanation:

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

Let theater's popcorn = P

nacho sales = N

$P\text{ }\alpha\text{ }\frac{1}{N}$

Equating the relationship:

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

when theater sales = $2,254

Nacho sales = $1,628

$\begin{gathered} 2254\text{ =}\frac{k}{1628} \\ k\text{ = 2254(1628)} \\ k\text{ = 3}669512 \end{gathered}$

The relationship becomes:

$P\text{ = }\frac{3669512}{N}$

When cost of the theater popcorn = $2,024

The cost from nachos = ?

We would use the relationship to get the above:

$\begin{gathered} 2024\text{ = }\frac{3669512}{N} \\ 2024N\text{ = 3669512}18 \\ N\text{ = }\frac{\text{3669512}}{2024} \\ N\text{ = }1813 \end{gathered}$

Hence, the employee earned $1813 from Nachos