Jill wants to have a bowling party with her friends. Normally, the local bowling alley charges $4 per person to bowl and $3 per person for shoe rentals. However, the alley also has a group rate of $90 for everyone to bowl, along with a discounted rate of $2 per person for shoe rentals.
) How many people would need to go to the party for the two options to cost the same?

Let's define $ x $ as the number of people attending the bowling party.

### Regular option costs:
- Cost of bowling: $4 per person.
- Cost of shoe rentals: $3 per person.

The total cost for $ x $ people under the regular option is:
\[
\text{Regular cost} = 4x + 3x = 7x
\]

### Group rate option costs:
- Group rate for bowling: $90 (fixed, regardless of the number of people).
- Discounted shoe rentals: $2 per person.

The total cost for $ x $ people under the group rate option is:
\[
\text{Group cost} = 90 + 2x
\]

### Setting the two options equal to find the break-even point:
\[
7x = 90 + 2x
\]

### Solving the equation:
1. Subtract $ 2x $ from both sides:
\[
7x - 2x = 90
\]
\[
5x = 90
\]

2. Divide both sides by 5:
\[
x = \frac{90}{5} = 18
\]

### Conclusion:
The two options will cost the same if **18 people** attend the party.

Would you like further details or have any questions?

Here are 5 related questions:
1. What would the total cost be for 18 people under both pricing plans?
2. How much would Jill save per person by choosing the group rate for 20 people?
3. What if the regular price for bowling increased to $5 per person?
4. How would the group rate change if the shoe rental fee were reduced to $1 per person?
5. How would the equation change if the group rate were set at $100 instead of $90?

**Tip:** When comparing two pricing structures, setting up an equation and finding where the costs are equal helps determine the break-even point.

Jill wants to have a bowling party with her friends. Normally, the local bowling alley charges $4 per person to bowl and $3 per person for shoe rentals. However, the alley also has a group rate of $90 for everyone to bowl, along with a discounted rate of $2 per person for shoe rentals. How many people would need to go to the party for the two options to cost the same?

Find out how many people need to attend Jill's bowling party for the regular pricing and group rate to cost the same. Explore the algebraic solution to this real-world problem using linear equations. Suitable for Grades 6-8 students.

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