Let's break down the problem step-by-step to formulate the system of inequalities.
1. Define the variables:
- Let [tex]\( t \)[/tex] represent the number of apple tarts the baker makes each day.
- Let [tex]\( p \)[/tex] represent the number of apple pies the baker makes each day.
2. Identify the constraints:
- Each tart requires 1 apple.
- Each pie requires 8 apples.
- The baker receives a shipment of 184 apples every day.
3. Formulating the first inequality:
- Given that the baker makes no more than 40 tarts per day, we can write:
[tex]\[
t \leq 40
\][/tex]
4. Formulating the second inequality:
- The total number of apples used for the tarts is [tex]\( t \)[/tex] (since each tart requires 1 apple).
- The total number of apples used for the pies is [tex]\( 8p \)[/tex] (since each pie requires 8 apples).
- Since the baker has a shipment of a total of 184 apples, the combined use of apples for pies and tarts must not exceed this number:
[tex]\[
t + 8p \leq 184
\][/tex]
Thus, combining these constraints, the system of inequalities that represents the possible number of pies [tex]\( p \)[/tex] and tarts [tex]\( t \)[/tex] the baker can make is:
[tex]\[
\begin{array}{l}
t \leq 40 \\
8p + t \leq 184
\end{array}
\][/tex]
