Jacob wants to hang out with friends at the bowling alley. The closest bowling alley he found offers lane rentals for $5.50 per hour from 10 a.m. until 5 p.m. After 5 p.m., prices jump to $7 per hour. If Jacob rents a lane for 3 hours starting at 4 p.m., how much will he have to pay?
The price of renting a lane from 4 p.m. is $7 per hour, so for 3 hours, Jacob will have to pay 7 * 3 = $<<7*3=21>>21.
Since the bowling alley offers a different price from 10 a.m. until 5 p.m., before 5 p.m. Jacob will pay 5.5 * 3 = $<<5.5*3=16.5>>16.5.
The cost of lane rental beginning at 4 p.m. will be 21 + 16.5 = $<<21+16.5=37.5>>37.5. Answer: \boxed{37.5}.
To calculate how much Jacob will have to pay, we need to consider two different price periods: before and after 5 p.m.
For the duration between 4 p.m. and 5 p.m., Jacob will have to pay the rate of $5.50 per hour, as this is before the prices jump. Since he will be renting a lane for 1 hour during this time, the cost for this period will be 1 * $5.50 = $5.50.
For the duration after 5 p.m., the rate increases to $7 per hour. Jacob will be renting a lane for 2 more hours during this time. So the cost for this period will be 2 * $7 = $14.
Now we add up the costs for both time periods to find the total cost: $5.50 + $14 = $19.50.
Therefore, Jacob will have to pay $19.50 to rent a lane for 3 hours starting at 4 p.m.