Question

Laura is buying bottles of water and bottles of lemonade for an event at her school . She needs to buy at least 6,400 ounces of beverages between the water and lemonade . Each bottle of water is 20 ounces, and each bottle of lemonade is 32 ounces . Laura has a budget of $600 to buy the beverages . The system of inequalities shown below represents this situation .

20x + 32y ≥ 6,400

1 .5x + 2 .5y ≤ 600

One solution to this system of inequalities is (40, 180) . What does this solution represent?

Answer 1

The solution (40, 180) means Laura plans to purchase 40 bottles of water and 180 bottles of lemonade, thereby meeting the minimum beverage requirement without exceeding her budget of $600.

Step-by-step explanation:

The solution (40, 180) to the system of inequalities represents Laura buying 40 bottles of water and 180 bottles of lemonade for the school event. The first inequality, 20x + 32y ≥ 6,400, ensures that the total ounces of beverages is at least 6,400 ounces. The second inequality, 1.5x + 2.5y ≤ 600, ensures that the total cost does not exceed her budget of $600. In this context, 'x' represents the number of water bottles, each 20 ounces, and 'y' represents the number of lemonade bottles, each 32 ounces.