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The owner of a new restaurant is designing its floor plan. His goal is to have a seating capacity of at least $460$ customers. The small tables can seat $3$ customers, while the large tables can seat $9$ customers. $\newline$ Select the inequality in standard form that describes this situation. Use the given numbers and the following variables. $\newline$ $x =$ the number of small tables $\newline$ $y =$ the number of large tables $\newline$ Choices: $\newline$ (A) $3 + x + 9 + y > 460$ $\newline$ (B) $3 + x + 9 + y \geq 460$ $\newline$ (C) $3x + 9y \geq 460$ $\newline$ (D) $3x + 9y > 460$

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Write a linear inequality: word problems

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Q. The owner of a new restaurant is designing its floor plan. His goal is to have a seating capacity of at least

460

customers. The small tables can seat

3

customers, while the large tables can seat

9

customers.

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of small tables

\newline

y =

the number of large tables

\newline

Choices:

\newline

(A)

3 + x + 9 + y > 460

\newline

(B)

3 + x + 9 + y \geq 460

\newline

(C)

3x + 9y \geq 460

\newline

(D)

3x + 9y > 460

Define Seating Capacity: The owner needs to have a seating capacity for at least $460$ customers. We need to find an inequality that represents this situation using the variables $x$ and $y$ , where $x$ is the number of small tables and $y$ is the number of large tables. Each small table seats $3$ customers, and each large table seats $9$ customers.
Calculate Total Capacity: To find the total seating capacity, we multiply the number of small tables $x$ by the number of customers each small table can seat $3$ , and the number of large tables $y$ by the number of customers each large table can seat $9$ . This gives us the total seating capacity as a function of the number of tables: $3x$ for small tables and $9y$ for large tables.
Combine Small and Large Tables: Adding the total seating capacity of small tables and large tables together, we get the expression $3x + 9y$ . This represents the total seating capacity based on the number of small and large tables.
Form Inequality: Since the goal is to have a seating capacity of at least $460$ customers, the total seating capacity must be greater than or equal to $460$ . Therefore, the inequality that represents this situation is $3x + 9y \geq 460$ .

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