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A baker makes apple tarts and apple pies each day. Each tart, [tex]\( t \)[/tex], requires 1 apple, and each pie, [tex]\( p \)[/tex], requires 8 apples. The baker receives a shipment of 184 apples every day. If the baker 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?

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

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

[tex]\[
t \leq 40
\][/tex]

[tex]\[
p + 8t \leq 184
\][/tex]

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



Answer :

GinnyAnswer
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]

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