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

2) Write an inequality that represents this description.

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.

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Answer 1

Let's break down the problem step by step.

1) Graph the inequalities in Desmos:

To graph this scenario, we will need to create an inequality based on the budget.

2) Write an inequality:

The total cost for attending is given by:

• Cost for entrance for x people: \( 15x \)
• Cost for bowling for y hours: \( 20y \)

The total cost should be less than or equal to the budget of $200. Thus, the inequality representing the situation is: \[ 15x + 20y \leq 200 \]

3) Cost for 7 people to attend for 3 hours:

To calculate the cost:

• Cost for 7 people: \( 15 \times 7 = 105 \)
• Cost for 3 hours: \( 20 \times 3 = 60 \)

Total cost = \( 105 + 60 = 165 \)

So, the total cost for 7 people to attend for 3 hours is $165.

4) Solving for 10 people for 2-hour bowling session:

Calculate the costs with \( x = 10 \) and \( y = 2 \):

• Cost for 10 people: \( 15 \times 10 = 150 \)
• Cost for 2 hours: \( 20 \times 2 = 40 \)

Total cost = \( 150 + 40 = 190 \)

Since \( 190 \leq 200 \), so yes, it is within the budget for 10 people for a 2-hour bowling session.

5) Solving for 8 people for 2-hour bowling session:

Calculate the costs with \( x = 8 \) and \( y = 2 \):

• Cost for 8 people: \( 15 \times 8 = 120 \)
• Cost for 2 hours: \( 20 \times 2 = 40 \)

Total cost = \( 120 + 40 = 160 \)

Since \( 160 \leq 200 \), so yes, it is within the budget for 8 people for a 2-hour bowling session.

Summary of Answers:

1. Inequality: \( 15x + 20y \leq 200 \)
2. Cost for 7 people for 3 hours: $165
3. 10 people for 2-hour session: within budget
4. 8 people for 2-hour session: within budget

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