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

Question

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 inequalities in Desmos. Click here to open Desmos (opens in a new tab).

2) Write an inequality that represents this description.
y=7x+3

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 solve this problem, we'll break it down into steps based on your provided information.

1. Inequality Representation: The total cost consists of the entrance fee for each person plus the hourly fee for the bowling session. Thus, the inequality can be represented as follows:

   Given:

   • Entrance cost per person: $15
   • Hourly cost: $20
   • Budget: $200

   The total cost is represented as: \[ C = 15x + 20y \] To express the cost being within budget: \[ 15x + 20y \leq 200 \]

2. Graphing the Inequality: You will need to graph the inequality \(15x + 20y \leq 200\) on Desmos. This will give you a visual representation of the combinations of people (x) and hours (y) that would keep the total cost within the budget.

3. Cost Calculation: For 7 people attending for 3 hours: \[ C = 15(7) + 20(3) \] \[ C = 105 + 60 \] \[ C = 165 \] So, the cost for 7 people to attend for 3 hours is $165.

4. Verifying the Budget for 10 People: For 10 people for an unknown number of hours \(y\): \[ 15(10) + 20y \leq 200 \] \[ 150 + 20y \leq 200 \] Subtracting 150 from both sides: \[ 20y \leq 50 \] Dividing by 20: \[ y \leq 2.5 \] So, 10 people can attend for 2.5 hours (2 hours and 30 minutes) within the $200 budget.

5. Verifying the Budget for 8 People: For 8 people for an unknown number of hours \(y\): \[ 15(8) + 20y \leq 200 \] \[ 120 + 20y \leq 200 \] Subtracting 120 from both sides: \[ 20y \leq 80 \] Dividing by 20: \[ y \leq 4 \] So, 8 people can attend for up to 4 hours within the $200 budget.

Summary Answers:

1. Cost for 7 people for 3 hours: $165
2. For 10 people: Up to 2.5 hours is within budget
3. For 8 people: Up to 4 hours is within budget

If you have any further questions or need assistance with other tasks, feel free to ask!