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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 460460 customers. The small tables can seat 33 customers, while the large tables can seat 99 customers.\newlineSelect the inequality in standard form that describes this situation. Use the given numbers and the following variables.\newlinex=x = the number of small tables\newliney=y = the number of large tables\newlineChoices:\newline(A) 3 + x + 9 + y > 460\newline(B) 3+x+9+y≥4603 + x + 9 + y \geq 460\newline(C) 3x+9y≥4603x + 9y \geq 460\newline(D) 3x + 9y > 460

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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 460460 customers. The small tables can seat 33 customers, while the large tables can seat 99 customers.\newlineSelect the inequality in standard form that describes this situation. Use the given numbers and the following variables.\newlinex=x = the number of small tables\newliney=y = the number of large tables\newlineChoices:\newline(A) 3+x+9+y>4603 + x + 9 + y > 460\newline(B) 3+x+9+y≥4603 + x + 9 + y \geq 460\newline(C) 3x+9y≥4603x + 9y \geq 460\newline(D) 3x+9y>4603x + 9y > 460
  1. Define Seating Capacity: The owner needs to have a seating capacity for at least 460460 customers. We need to find an inequality that represents this situation using the variables xx and yy, where xx is the number of small tables and yy is the number of large tables. Each small table seats 33 customers, and each large table seats 99 customers.
  2. Calculate Total Capacity: To find the total seating capacity, we multiply the number of small tables xx by the number of customers each small table can seat 33, and the number of large tables yy by the number of customers each large table can seat 99. This gives us the total seating capacity as a function of the number of tables: 3x3x for small tables and 9y9y for large tables.
  3. Combine Small and Large Tables: Adding the total seating capacity of small tables and large tables together, we get the expression 3x+9y3x + 9y. This represents the total seating capacity based on the number of small and large tables.
  4. Form Inequality: Since the goal is to have a seating capacity of at least 460460 customers, the total seating capacity must be greater than or equal to 460460. Therefore, the inequality that represents this situation is 3x+9y≥4603x + 9y \geq 460.

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