Question

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?
people

Answer 1

Let's denote the number of people attending the bowling party as \( n \).

### Option 1: Normal Rates
For the normal rates, the cost per person for bowling is $4 and for shoe rentals is $3. Therefore, the total cost for \( n \) people is:

\[
\text{Total Cost}_1 = n \times (4 + 3) = n \times 7 = 7n
\]

### Option 2: Group Rate
For the group rate, there is a flat fee of $90 for bowling for everyone, and the shoe rental is discounted to $2 per person. Therefore, the total cost for \( n \) people is:

\[
\text{Total Cost}_2 = 90 + n \times 2 = 90 + 2n
\]

### Setting the Costs Equal
To find out how many people are needed for the two options to cost the same, we set the total costs equal to each other:

\[
7n = 90 + 2n
\]

### Solving for \( n \)
Subtract \( 2n \) from both sides:

\[
7n - 2n = 90
\]
\[
5n = 90
\]

Now divide both sides by 5:

\[
n = \frac{90}{5} = 18
\]

### Conclusion
The number of people that would need to go to the party for the two options to cost the same is \( \boxed{18} \).