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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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1 answer

To help you with this problem, let's break it down step by step.

Step 1: Write the inequality.

The total cost for the event can be represented by the equation:

\[ \text{Total Cost} = (15 \cdot x) + (20 \cdot y) \]

Here, \(15 \cdot x\) represents the entrance fee for \(x\) people, and \(20 \cdot y\) represents the hourly charge for \(y\) hours. Since the budget for the event is $200, the inequality representing this situation would be:

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

Step 2: Calculate the cost for 7 people attending for 3 hours.

For \(x = 7\) and \(y = 3\):

\[ \text{Total Cost} = (15 \cdot 7) + (20 \cdot 3) \] \[ = 105 + 60 \] \[ = 165 \]

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

Step 3: Check if 10 people for a certain number of hours is within the $200 budget.

To determine if the cost for 10 people will fit within the budget, we need to find the maximum \(y\) (number of hours) such that:

\[ 15(10) + 20y \leq 200 \] \[ 150 + 20y \leq 200 \] \[ 20y \leq 200 - 150 \] \[ 20y \leq 50 \] \[ y \leq \frac{50}{20} \] \[ y \leq 2.5 \]

Therefore, for 10 people, they would be able to bowl for 2.5 hours or less to stay within the budget.

Step 4: Check if 8 people for a certain number of hours is within the $200 budget.

Next, let's check if 8 people can bowl for a certain number of hours while staying under the budget:

\[ 15(8) + 20y \leq 200 \] \[ 120 + 20y \leq 200 \] \[ 20y \leq 200 - 120 \] \[ 20y \leq 80 \] \[ y \leq \frac{80}{20} \] \[ y \leq 4 \]

Thus, for 8 people, they can bowl for up to 4 hours while remaining within the budget.

Summary of Answers:

  1. The inequality is \(15x + 20y \leq 200\).
  2. The cost for 7 people for 3 hours is $165.
  3. For 10 people, they can bowl for up to 2.5 hours (within budget).
  4. For 8 people, they can bowl for up to 4 hours (within budget).

If you need further clarification or assistance, feel free to ask!