Question

A restaurant offers two meal options for parties: a chicken meal and a vegetarian meal. It provides meals for two companies that each pay the same amount per meal.

Company A pays $320 for 20 chicken meals and 15 vegetarian meals.
Company B pays $580 for 22 chicken meals and 45 vegetarian meals.

Part A Which system of equations can be used to find the cost of each chicken meal x in dollars and the cost of each vegetarian meal y in dollars?

Answer 1

To determine the costs of chicken and vegetarian meals, a system of linear equations can be created: 20x + 15y = $320 for Company A and 22x + 45y = $580 for Company B. Solving these will give the meal costs.

Step-by-step explanation:

To find the cost of each chicken meal (x in dollars) and the cost of each vegetarian meal (y in dollars), we need to set up a system of linear equations based on the information given for both companies' meal purchases.

For Company A, the equation reflecting the cost is 20x + 15y = $320. For Company B, the equation reflecting the cost is 22x + 45y = $580. These equations correspond to the number of chicken and vegetarian meals multiplied by their respective costs which sum up to the total amount paid by each company.

To solve these equations, you would typically use methods such as substitution or elimination to find the values of x and y that satisfy both equations simultaneously.