To determine how many cupcakes and pizza pies you can buy given the constraints of the problem, we will formulate a system of inequalities.
Let's denote:
- [tex]\( c \)[/tex] as the number of cupcakes,
- [tex]\( p \)[/tex] as the number of pizza pies.
The constraints given in the problem are:
1. Each pizza pie costs [tex]$12, and you need at least 5 pizza pies. This can be written as:
\[
p \geq 5
\]
2. Each cupcake costs \$[/tex]3.
3. You cannot spend more than \[tex]$100 in total. The total cost of cupcakes and pizza pies should not exceed $[/tex]100. This can be written as:
[tex]\[
3c + 12p \leq 100
\][/tex]
Therefore, the system of inequalities that represents this situation is:
[tex]\[
\begin{array}{l}
p \geq 5 \\
3c + 12p \leq 100
\end{array}
\][/tex]
Among the given options, the one that matches our system of inequalities is:
D. [tex]\( p \geq 5, 3c + 12p \leq 100 \)[/tex]
So, the correct answer is:
D. [tex]\( p \geq 5, 3c + 12p \leq 100 \)[/tex]
