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Question

Question
Tommy is organizing a field trip to Stars and Strikes Bowling with his friends.

The budget for the event is $200. Stars and Strikes Bowling charges $15 per person for entrance and $20 per hour.

Let x represent the number of people attending and let y represent the number of hours spent.





Complete the statements below.

(1 point)
1) Graph this system of inequalities in Desmos. Click here to open Desmos.

2) Write an inequality that represents this description. Use the inequality symbols ≥ ≤ > <

2) How much will it cost for 7 people to attend for 3 hours? $

3) Solving the equation representing this situation proves that 10 people for exactly
-hour bowling session is within the $200 budget.

3) Solving the equation representing this situation proves that 8 people for exactly
-hour bowling session is within the $200 budget.

Answer 1

To help you with the problem involving Tommy's field trip to Stars and Strikes Bowling, let’s break this down step-by-step.

1. Setting Up the Inequality:

   • The cost for each person is $15, so for \( x \) people, the cost is \( 15x \).
   • The cost for renting the bowling lane for \( y \) hours is $20 per hour, which is \( 20y \).
   • The total cost must be less than or equal to the budget of $200.

   Therefore, the inequality representing this situation is: \[ 15x + 20y \leq 200. \]

2. Calculating the Cost for 7 People for 3 Hours:

   • For \( x = 7 \) and \( y = 3 \): \[ \text{Total Cost} = 15(7) + 20(3) = 105 + 60 = 165. \] Therefore, the cost for 7 people to attend for 3 hours is $165.

3. Checking Budget for 10 People:

   • For \( x = 10 \) and let's say \( y = 1 \) (assuming that's what you meant by "exactly -hour bowling session"): \[ \text{Total Cost} = 15(10) + 20(1) = 150 + 20 = 170. \] Since $170 is within the $200 budget, this situation confirms that 10 people for exactly 1 hour is within the budget.

4. Checking Budget for 8 People:

   • For \( x = 8 \) and let's say \( y = 4 \) (assuming you meant "exactly -hour bowling session"):

   \[ \text{Total Cost} = 15(8) + 20(4) = 120 + 80 = 200. \] Since $200 matches the budget exactly, this confirms that 8 people for exactly 4 hours is on the budget.

Summary of Answers:

1. The inequality is \( 15x + 20y \leq 200 \).
2. Cost for 7 people for 3 hours: $165.
3. 10 people for exactly 1 hour is within the budget.
4. 8 people for exactly 4 hours is on budget.

If you need further assistance, or to graph the inequalities on Desmos, simply input the following equation:

\[ 15x + 20y \leq 200 \]

This will show you the feasible region for this event.