if t represent the number of tickets purchased for a baseball game, which scenario is modeled by the…

if t represent the number of tickets purchased for a baseball game, which scenario is modeled by the equation, 32.50t + 5 = 28.75t + 20, to determine the number of tickets that result in the same cost for both levels?\nthe price for the lower level is $5.00 a ticket, plus $32.50 for a discounted parking pass. the middle - level tickets are $20 each, plus $28.75 for a parking pass.\nthe price for the lower level is $32.50 a ticket, plus $5.00 for a discounted parking pass. the middle - level tickets are $28.75 each, plus $20.00 for a parking pass.\nthe price for the lower level is $28.75 a ticket, plus $20.00 for a parking pass. the middle - level tickets are $32.50 each, plus $5.00 for a discounted parking pass.\nthe price for the lower level is $20 each, plus $28.75 for a parking pass. the middle - level tickets are $32.50 each, plus $5.00 for a discounted parking pass.

if t represent the number of tickets purchased for a baseball game, which scenario is modeled by the equation, 32.50t + 5 = 28.75t + 20, to determine the number of tickets that result in the same cost for both levels?\nthe price for the lower level is $5.00 a ticket, plus $32.50 for a discounted parking pass. the middle - level tickets are $20 each, plus $28.75 for a parking pass.\nthe price for the lower level is $32.50 a ticket, plus $5.00 for a discounted parking pass. the middle - level tickets are $28.75 each, plus $20.00 for a parking pass.\nthe price for the lower level is $28.75 a ticket, plus $20.00 for a parking pass. the middle - level tickets are $32.50 each, plus $5.00 for a discounted parking pass.\nthe price for the lower level is $20 each, plus $28.75 for a parking pass. the middle - level tickets are $32.50 each, plus $5.00 for a discounted parking pass.

Answer

  1. First, set up the cost - equations for each level:
    • Let (t) be the number of tickets.
    • For the lower - level tickets, assume the cost per ticket is (x) and the parking pass cost is (y). The total cost for the lower - level is (C_{lower}=xt + y).
    • For the middle - level tickets, assume the cost per ticket is (a) and the parking pass cost is (b). The total cost for the middle - level is (C_{middle}=at + b).
    • We are given the equation (32.5t + 5=28.75t + 20).
  2. Then, solve the equation for (t):
    • Subtract (28.75t) from both sides of the equation:
      • (32.5t-28.75t + 5=28.75t-28.75t + 20).
      • (3.75t+5 = 20).
    • Subtract 5 from both sides:
      • (3.75t+5 - 5=20 - 5).
      • (3.75t=15).
    • Divide both sides by 3.75:
      • (t=\frac{15}{3.75}=4).
  3. Now, let's check the cost expressions for each option to see which one satisfies the equation:
    • Option 1: If the price for the lower - level is (x = 28.75) and the parking pass is (y = 20), and the price for the middle - level is (a = 32.5) and the parking pass is (b = 5).
      • The cost for the lower - level (C_{lower}=28.75t + 20).
      • The cost for the middle - level (C_{middle}=32.5t + 5).
      • When (t = 4), (C_{lower}=28.75\times4+20=115 + 20=135).
      • (C_{middle}=32.5\times4+5=130 + 5=135).

Explanation:

Step1: Set up the cost - equations

We set up the cost equations for lower and middle - level tickets based on the general form (C = \text{cost per ticket}\times\text{number of tickets}+\text{parking pass cost}).

Step2: Solve the given equation for (t)

We perform algebraic operations (subtraction and division) to find the number of tickets (t) that makes the two cost expressions equal.

Step3: Check the options

We substitute (t = 4) into the cost expressions for each option to find the correct one.

Answer: The price for the lower level is $28.75 a ticket, plus $20.00 for a parking pass. The price for the middle - level is $32.50 a ticket, plus $5.00 for a parking pass.