a restaurant wishes to have at least one server for every 12 tables. each of the tables in the restaurant…

a restaurant wishes to have at least one server for every 12 tables. each of the tables in the restaurant seats four guests. if x is the number of servers and y is the number of guests, which inequality represents the restaurants desired relationship of the number of servers to the number of guests?\n$x\\geq48y$\n$x\\geq3y$\n$3x\\geq y$\n$48x\\geq y$

a restaurant wishes to have at least one server for every 12 tables. each of the tables in the restaurant seats four guests. if x is the number of servers and y is the number of guests, which inequality represents the restaurants desired relationship of the number of servers to the number of guests?\n$x\\geq48y$\n$x\\geq3y$\n$3x\\geq y$\n$48x\\geq y$

Answer

Explanation:

Step1: Relate servers to tables

Each server covers ≤12 tables, so total tables ≤12x.

Step2: Relate tables to guests

Each table seats 4 guests, so total guests y = 4×(total tables). Rearranged, total tables = $\frac{y}{4}$.

Step3: Set up inequality

Substitute tables into server limit: $\frac{y}{4} \leq 12x$

Step4: Simplify the inequality

Multiply both sides by 4: $y \leq 48x$, or $48x \geq y$

Answer:

48x≥y