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 down the components of the problem:

1) **Inequality for Budget**:
The total cost for the event consists of the entrance fees for \(x\) people and the hourly bowling charge for \(y\) hours. The cost can be expressed as:
\[
15x + 20y \leq 200
\]

2) **Calculating the Cost for 7 People for 3 Hours**:
Plugging \(x = 7\) and \(y = 3\) into the cost equation:
\[
\text{Total Cost} = 15(7) + 20(3)
\]
Calculate each part:
\[
15(7) = 105 \quad \text{and} \quad 20(3) = 60
\]
Now sum those amounts:
\[
105 + 60 = 165
\]
Therefore, the cost for 7 people to attend for 3 hours is **$165**.

3) **For 10 People and Hours**:
To determine if 10 people can attend for an exact duration that is within the budget, let's set \(x = 10\) and calculate a suitable \(y\):
\[
15(10) + 20y \leq 200
\]
Simplifying:
\[
150 + 20y \leq 200
\]
Subtracting 150 from both sides:
\[
20y \leq 50
\]
Dividing both sides by 20:
\[
y \leq 2.5
\]
This indicates that 10 people can bowl for **at most 2.5 hours** while staying within the budget.

4) **For 8 People**:
Now we set \(x = 8\) and find an appropriate \(y\):
\[
15(8) + 20y \leq 200
\]
Simplifying:
\[
120 + 20y \leq 200
\]
Subtracting 120 from both sides:
\[
20y \leq 80
\]
Dividing both sides by 20:
\[
y \leq 4
\]
This indicates that 8 people can bowl for **up to 4 hours** while staying within the budget.

To summarize:
- The inequality is \(15x + 20y \leq 200\).
- The cost for 7 people for 3 hours is **$165**.
- For 10 people, they can have up to **2.5 hours**.
- For 8 people, they can have up to **4 hours**.