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 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.

Answer 1

Let’s break this down step by step for Tommy’s field trip to Stars and Strikes Bowling.

### 1) Inequality for the Situation:

Tommy is working with the following costs:

- Entrance fee: $15 per person
- Hourly fee for bowling: $20 per hour

The total cost can be represented as:

Total Cost = Entrance Fee + Hourly Fee
Total Cost = \( 15x + 20y \)

The budget constraint is $200, so we set up the inequality:

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

### 2) Cost Calculation:

Now, to find out how much it will cost for 7 people to attend for 3 hours, we just plug in the values into the total cost formula.

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

Total Cost = \( 15(7) + 20(3) \)
Total Cost = \( 105 + 60 = 165 \)

The cost for 7 people to attend for 3 hours will be **$165**.

### 3) Solving Inequalities:

For the statements about being within the $200 budget, we can generate equations and verify those situations.

**For 10 people for an unspecified number of hours, let’s denote hours as \( y \)**:
The total cost will be:

\[ 15(10) + 20y \leq 200 \]
\[ 150 + 20y \leq 200 \]
\[ 20y \leq 50 \]
\[ y \leq 2.5 \]

- Therefore, if Tommy has **10 people**, they can bowl for **2.5 hours** or less to stay within budget.

**For 8 people for an unspecified number of hours, let’s denote hours as \( y \)**:
The total cost will be:

\[ 15(8) + 20y \leq 200 \]
\[ 120 + 20y \leq 200 \]
\[ 20y \leq 80 \]
\[ y \leq 4 \]

- So, if Tommy has **8 people**, they can bowl for **4 hours** or less to stay within budget.

### Summary:

1) The inequality to graph is: \( 15x + 20y \leq 200 \).

2) The cost for 7 people to attend for 3 hours is **$165**.

3) The inequality checks prove that:
- **10 people for up to 2.5 hours** is under the budget.
- **8 people for up to 4 hours** is also under the budget.

Feel free to graph this on Desmos using the inequality provided!