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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 $251$ 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) $3x + 9y \leq 251$ $\newline$ (B) $3x + 9y > 251$ $\newline$ (C) $3x + 9y < 251$ $\newline$ (D) $3x + 9y \geq 251$

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Write a linear inequality: word problems

Full solution

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

251

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)

3x + 9y \leq 251

\newline

(B)

3x + 9y > 251

\newline

(C)

3x + 9y < 251

\newline

(D)

3x + 9y \geq 251

Calculate Small Tables Capacity: Small tables seat $3$ customers each, so the total seating capacity from small tables is $3$ times the number of small tables. $\newline$ Calculation: $3 \times x = 3x$
Calculate Large Tables Capacity: Large tables seat $9$ customers each, so the total seating capacity from large tables is $9$ times the number of large tables. $\newline$ Calculation: $9 \times y = 9y$
Calculate Total Seating Capacity: The total seating capacity is the sum of the seating capacity from small and large tables. $\newline$ Calculation: $3x + 9y$
Set Seating Capacity Goal: The goal is to have a seating capacity of at least $251$ customers. The inequality that represents this situation is the total seating capacity must be greater than or equal to $251$ . Calculation: $3x + 9y \geq 251$

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