Let's break down the problem step-by-step to determine the correct system of inequalities.
1. Understanding the Variables and Resources:
- [tex]\( t \)[/tex] represents the number of apple tarts made daily.
- [tex]\( p \)[/tex] represents the number of apple pies made daily.
- Each tart requires 1 apple.
- Each pie requires 8 apples.
- The baker receives 184 apples per day.
2. Constraints Due to Daily Production Limits:
- The baker can make no more than 40 tarts per day. So, we have the inequality:
[tex]\[
t \leq 40
\][/tex]
3. Apples Usage Constraint:
- Each tart uses 1 apple and each pie uses 8 apples. The total apples used for both tarts and pies should not exceed the daily shipment of 184 apples. Hence, the inequality for the total usage of apples is:
[tex]\[
p + 8t \leq 184
\][/tex]
Combining these two constraints, we get the following system of inequalities:
[tex]\[
\begin{aligned}
t & \leq 40 \\
p + 8t & \leq 184
\end{aligned}
\][/tex]
This system ensures that the baker adheres to both the maximum number of tarts they can produce and the total number of apples available daily.
Thus, the correct answer is:
[tex]\[
\begin{aligned}
t & \leq 40 \\
p + 8t & \leq 184
\end{aligned}
\][/tex]
