Question

Marie is buying dinners for a work party. Let x be the number of vegetarian meals and y be the number of meals with meat. Which of the following systems of inequalities represents the given situation?

a. 16x + 19y ≤ 700, x ≥ 15, x + y > 35
b. 19x + 16y ≤ 700, x ≥ 15, x + y > 35
c. 16x + 19y ≤ 700, x ≤ 15, x + y > 35
d. 16x + 19y ≥ 700, x ≥ 15, x + y > 35

Answer 1

The correct system of inequalities for Marie's dinner purchase scenario is option a, which includes the constraints on the meal costs, vegetarian meal count, and total meal count.

Step-by-step explanation:

The system of inequalities that represents the situation where Marie is buying dinners for a work party, with x being the number of vegetarian meals and y being the number of meals with meat, is a. 16x + 19y ≤ 700, x ≥ 15, x + y > 35.

This system accounts for the costs of the meals, specifying that the total cost of x vegetarian meals and y meat meals should not exceed $700, that there has to be at least 15 vegetarian meals, and that the total number of meals should be more than 35.