Final answer:
To determine the maximum number of hospital supply boxes fitting the budget with 45 tear gas boxes purchased, we define X as the number of hospital supply boxes and Y as the number of tear gas boxes. We use the inequality BX + TY ≤ M, inserting hypothetical costs for B and T, and the total budget M to calculate the value of X, which is the number of hospital supply boxes.
Step-by-step explanation:
The scenario describes a situation where the NYC Mayor is managing budgets for the NYPD and hospitals. To represent this situation with a system of inequalities, let's define X as the number of hospital supply boxes and Y as the number of tear gas boxes. We do not have the specific budget constraints, so we will assume hypothetical prices for these items.
Let's say each hospital supply box costs $B and each tear gas box costs $T. If the total budget is $M, we would have the following inequality
$$B \cdot X + T \cdot Y \leq M$$
To find the maximum number of hospital supply boxes that can be purchased if 45 tear gas boxes are already bought, we replace Y with 45 and solve for X, given the inequality:
$$B \cdot X + T \cdot 45 \leq M$$
Solving for X gives us the maximum number of hospital supply boxes.
For the example of Mayor Bill de Blasio, we will choose hypothetical values for B, T, and M to illustrate the concept. For instance, if each hospital supply box costs $100 (B=$100), each tear gas box costs $50 (T=$50), and the budget is $10,000 (M=$10,000), then the maximum number of hospital supply boxes can be calculated as follows:
$$100X + 50 \cdot 45 \leq 10,000$$
$$100X + 2,250 \leq 10,000$$
$$100X \leq 7,750$$
$$X \leq 77.5$$
The maximum number of hospital supply boxes that fit into the budget, with 45 tear gas boxes already purchased, is 77. Of course, since you cannot purchase half a supply box, the actual maximum would be 77 boxes.