Question

Let x be the number of small groups and y be the number of larger groups. Which system of inequalities represents this situation?

A restaurant with 75 tables has 25 tables for small groups (couples or singles) and 50 tables for larger ones. Small groups can be seated at any table but larger groups have to wait for an opening.
Click on the correct answer.
A. xs 25 and x + ys 75
B. ya 50 and x + y s 75
C. x2 25 and x + y s 75
D. y s 50 and x + y s 75

Answer 1

The system of inequalities that represents the situation in the restaurant is option D: 'y ≤ 50 and x + y ≤ 75'. This indicates that the number of larger groups is limited to 50, and the total number of groups can't exceed 75 tables.

Step-by-step explanation:

The student is asking for the system of inequalities that represents a situation in a restaurant with a limited number of tables for small and larger groups.

The correct answer to the question is option D. The inequality y ≤ 50 signifies that the number of larger groups (y) that can be seated cannot exceed 50 because there are only 50 tables available for them. The inequality x + y ≤ 75 denotes that the combined number of small and large groups (x + y) cannot exceed 75, which is the total number of tables in the restaurant. It's important to note that small groups can be seated at any table, implying that all 75 tables could potentially be used for small groups if no larger groups are present. However, larger groups are limited to their specific tables, hence the exclusive limit on y.