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A baker makes apple tarts ([tex]$t$[/tex]) and apple pies ([tex]$p$[/tex]) each day. Each tart requires 1 apple, and each pie requires 8 apples. The baker receives a shipment of 184 apples every day and makes no more than 40 tarts per day.

Which system of inequalities can be used to find the possible number of pies and tarts the baker can make?

A.
[tex]\[
\begin{array}{c}
t \leq 40 \\
p \leq 184 \\
t \leq 40 \\
8 p \leq 184
\end{array}
\][/tex]

B.
[tex]\[
\begin{aligned}
t & \leq 40 \\
p + 8t & \leq 184
\end{aligned}
\][/tex]

C.
[tex]\[
\begin{array}{c}
t \leq 40 \\
8p + t \leq 184
\end{array}
\][/tex]



Answer :

GinnyAnswer
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]

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