Question

here are two equations that we considered in this lesson about subway capacity.

• r is the seating capacity.
• d is the standing capacity.

pick two numbers and explain what they mean in this situation.
6 2 600 100 -1/3

Explanation:

Step1: Analyze the number 6

In the equation \(6t + 2d=600\), the coefficient 6. Since \(t\) is the seating capacity, 6 represents the number of seats per subway car.

Step2: Analyze the number 2

In the equation \(6t + 2d = 600\), the coefficient 2. Since \(d\) is the standing capacity, 2 represents the number of standing - room areas per subway car.

Step3: Analyze the number 600

In the equation \(6t + 2d=600\), the constant 600. It represents the total capacity (seating + standing) of a subway car.

Step4: Analyze the number 100

In the equation \(t = 100-\frac{1}{3}d\), the constant 100. When \(d = 0\) (no standing passengers), \(t=100\), so 100 represents the maximum seating capacity of the subway car.

Step5: Analyze the number \(-\frac{1}{3}\)

In the equation \(t = 100-\frac{1}{3}d\), the coefficient \(-\frac{1}{3}\). It represents the rate at which the seating capacity \(t\) decreases as the standing capacity \(d\) increases. For every 3 additional standing passengers, the number of available seats decreases by 1.

Answer:

• 6: Number of seats per subway car.
• 2: Number of standing - room areas per subway car.
• 600: Total capacity (seating + standing) of a subway car.
• 100: Maximum seating capacity of the subway car.
• \(-\frac{1}{3}\): Rate at which seating capacity decreases as standing capacity increases (for every 3 additional standing passengers, 1 seat is 'lost').