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?
A. [tex]
\begin{array}{c}
t \leq 40 \\
p \leq 184
\end{array}
[/tex]
B. [tex]
t \leq 40 \\
8 p \leq 184
[/tex]
C. [tex]
t \leq 40 \\
p+8 t \leq 184
[/tex]
D. [tex]
t \leq 40 \\
8 p+t \leq 184
[/tex]
Answer (1)
The number of tarts, t , is no more than 40: t ≤ 40 .
The total number of apples used for tarts and pies does not exceed 184: 8 p + t ≤ 184 .
Combine the inequalities to form the system.
The system of inequalities is t ≤ 40 ; 8 p + t ≤ 184 .
Explanation
Problem Analysis Let's analyze the given problem. We are given that the baker makes apple tarts and apple pies each day. Each tart, t , requires 1 apple, and each pie, p , requires 8 apples. The baker receives a shipment of 184 apples every day. The baker makes no more than 40 tarts per day. We need to find the system of inequalities that can be used to find the possible number of pies and tarts the baker can make.
Tarts Inequality The number of tarts is limited to 40, so we have the inequality t l e q 40 .
Apples Inequality The total number of apples used for tarts and pies cannot exceed 184. Each tart uses 1 apple and each pie uses 8 apples. So, the total number of apples used is t + 8 p . Therefore, we have the inequality t + 8 p l e q 184 , which can also be written as 8 p + t l e q 184 .
Final System of Inequalities Combining the two inequalities, we get the system of inequalities:
t l e q 40
8 p + t l e q 184
Comparing this with the given options, we see that the correct option is:
t l e q 40
8 p + t l e q 184
Examples
Imagine you're planning a bake sale. You want to figure out how many apple tarts and pies you can make with the ingredients you have. This problem helps you set limits based on the number of apples you have and how many tarts you can realistically bake. By understanding these constraints, you can maximize your profits and avoid wasting ingredients. This is a practical application of inequalities in everyday planning.
