Let's solve the problem step-by-step.
Given that the baker makes apple tarts (denoted by [tex]\( t \)[/tex]) and apple pies (denoted by [tex]\( p \)[/tex]):
1. Each tart requires 1 apple.
2. Each pie requires 8 apples.
3. The baker receives a shipment of 184 apples every day.
4. The baker makes no more than 40 tarts per day.
We need to find a system of inequalities that models these constraints.
### Step 1: Total number of apples constraint
Each day, the baker can use at most 184 apples, utilized by tarts and pies. Therefore, the total apple usage is:
[tex]\[ p + 8t \leq 184 \][/tex]
### Step 2: Maximum tarts constraint
The baker can make no more than 40 tarts per day. Hence, the maximum number of tarts is:
[tex]\[ t \leq 40 \][/tex]
### Step 3: Pies and additional apples constraints
Additionally, if we rearrange the usage of apples to emphasize pies, another form of the inequality shows:
[tex]\[ 8p + t \leq 184 \][/tex]
### Summary
Therefore, the constraints can be summarized in the following system of inequalities, which best capture the baker's daily production limits:
[tex]\[
\begin{aligned}
p + 8t & \leq 184 \\
t & \leq 40 \\
8p + t & \leq 184
\end{aligned}
\][/tex]
So, the correct system of inequalities that describes the possible number of pies and tarts the baker can make per day is:
[tex]\[
\begin{aligned}
p+8t & \leq 184 \\
t & \leq 40 \\
8p+t & \leq 184
\end{aligned}
\][/tex]
