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 \( \boxed{18} \).