Question

Joseph and his children went into a movie theater where they sell bags of popcorn for $7.50 each and pretzels for $4.75 each. Joseph has 595 to spend and must buy no less than 16 bags of popcorn and pretzels altogether. If z represents the number of bags of popcorn purchased and y represents the number of pretzels purchased, write and solve a sstem of inequalities graphically and determine one possible solution.

Answer 1

We will have the following system of inequalities:

`\begin{cases}z+y\ge16 \\ 7.50z+4.75y\le595\end{cases}`

This graphically is:

So, the solutions will be located at the intersection of both graphs. So, one possible solution is:

5 bags of popcorn and 15 bags of pretzels. This solution can be seen in the following graph: