Gabrielle is baking large batches of brownies and cookies to share with her friends and family. Among other ingredients, her brownie recipe calls for 1 cup of sugar and 2 eggs and her cookie recipe calls for 3 cups of sugar and 2 eggs. Gabrielle has 20 eggs and 21 cups of sugar, and she would like to know how many batches of brownies and cookies she can bake without getting more of these ingredients.
Which system of inequalities can model Gabrielle’s situation, where x represents batches of brownies and y represents batches of cookies?
A. 2x + 3y ≥ 20
x + 2y ≥ 21
B. 2x + 2y ≥ 20
x + 3y ≥ 21
C. 2x + 3y ≤ 20
x + 2y ≤ 21
D. 2x + 2y ≤ 20
x + 3y ≤ 21
The correct system of inequalities that can model Gabrielle's situation is:
A. 2x + 3y ≥ 20
x + 2y ≥ 21
This is because the brownie recipe requires 2 eggs and 1 cup of sugar, and the cookie recipe requires 2 eggs and 3 cups of sugar. Therefore, the inequalities should reflect these requirements.