High School

A carpentry shop makes dinner tables and coffee tables. Each week, the shop must complete at least 9 dinner tables and 13 coffee tables to be shipped to furniture stores. If the shop sells dinner tables for $120 and coffee tables for $150, write a system of inequalities to describe all possible ways the shop can earn at least $3200.

Note: \( d \) = number of dinner tables, \( c \) = number of coffee tables

A.
\[
\begin{align*}
d & \geq 9 \\
c & \geq 13 \\
120d + 150c & < 3200
\end{align*}
\]

B.
\[
\begin{align*}
d & \geq 9 \\
c & \geq 13 \\
120d + 150c & \geq 3200
\end{align*}
\]

C.
\[
\begin{align*}
d & \geq 9 \\
c & \geq 13 \\
120d + 213 & < 3200
\end{align*}
\]

D.
\[
\begin{align*}
d & \leq 9 \\
c & \geq 13 \\
120d + 150c & > 3200
\end{align*}
\]

Answer :

Final answer:

The correct choice is B. The system of inequalities is d ≥ 9, c ≥ 13, and 120d + 150c ≥ 3200.

Explanation:

The correct choice for the given question is B. The system of inequalities that describes all possible ways the shop can earn at least $3200 is:

d ≥ 9

c ≥ 13

120d + 150c ≥ 3200

These inequalities ensure that the shop makes at least 9 dinner tables and 13 coffee tables, and the total earnings from the sales of these tables are equal to or greater than $3200.

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