Answer:
Explanation:
To solve this problem, let's start by defining the variables xx and yy as the number of cupcakes and cookies purchased, respectively. The cost of each cupcake is $5 and the cost of each cookie is $0.50. Easton has $50 to spend, so we can write the following inequality to represent the total cost of the cupcakes and cookies: 5x + 0.50y ≤ 50 Next, we know that Easton must buy at least 15 cupcakes and cookies altogether. This can be represented by the inequality: x + y ≥ 15 To solve this system of inequalities graphically, we can plot the feasible region on a coordinate plane. The feasible region is the set of all (x, y) pairs that satisfy both inequalities. To graph the inequality 5x + 0.50y ≤ 50, we can rearrange it to the standard form: y ≤ 100 - 10x We can start by plotting the line y = 100 - 10x, which represents the boundary of the inequality. Then, we shade the region below the line, including the line itself, since we want y to be less than or equal to the right side of the inequality. Next, let's graph the inequality x + y ≥ 15. Rearranging it to the standard form, we get: y ≥ 15 - x We can plot the line y = 15 - x, which represents the boundary of the inequality. Then, we shade the region above the line, including the line itself, since we want y to be greater than or equal to the right side of the inequality. The feasible region is the overlapping shaded region. One possible solution would be any point within this region. For example, (10, 5) would be a valid solution since it satisfies both inequalities. Remember that there are other possible solutions within the feasible region. You can explore different points within the shaded region to find other valid solutions.