Question

Mike wants to fence in part of his backyard. Joshua wants to burn at least 400 calories per day but no more than 600. Assuming he burns 4 calories per minute walking (w) and 5 calories per minute playing basketball (b), the situation can be modeled using these inequalities:

15w + 20b ≥ 400
15w + 20b ≤ 600

Answer 1

To find the combination of walking and playing basketball that satisfies the inequalities, plot the boundary lines and shade the feasible region. Then, identify the solution points that meet Joshua's goal of burning calories.

Step-by-step explanation:

To solve the system of inequalities, we can graph the boundary lines and shade the feasible region where the two inequalities overlap. Let's start by graphing the boundary line for the first inequality 15w + 20b ≥ 400. Rearranging the equation, we get w = (-20/15)b + (400/15). Now, we can plot this line on a graph. Similarly, for the second inequality 15w + 20b ≤ 600, rearranging the equation gives w = (-20/15)b + (600/15). Plot this line as well. The feasible region is the shaded area where the two lines intersect.

Next, let's consider the possible solution points within the feasible region. Each point represents a combination of walking (w) and playing basketball (b) that satisfies both inequalities. For example, if we choose the point (10, 10), it means that Mike can walk for 10 minutes and play basketball for 10 minutes, and this combination will meet Joshua's goal of burning at least 400 calories but no more than 600 calories.