Let x be the number of guests you can invite to the party and let y be the price per bowler.
For Bowling A:
y = $10.50
Total cost = x * y
For Bowling B:
y = $15.00
Total cost = x * y
To calculate how many guests you can invite to each bowling alley:
For Bowling A:
Total cost = $500
10.50x = 500
x = 500 / 10.50
x ≈ 47 guests
For Bowling B:
Total cost = $500
15x = 500
x = 500 / 15
x ≈ 33 guests
Therefore, you can invite up to 47 guests to Bowling Alley A and up to 33 guests to Bowling Alley B within the budget of $500.