Final answer:
Fred can afford to take an Uber for up to 6 miles to his sister's house with his $20 budget after accounting for a $5 one-time fee and $2.50 per mile charge.
Step-by-step explanation:
To determine the maximum number of miles Fred can be from his sister's house to afford an Uber ride with his $20 budget, we have to account for both the one-time fee and the per-mile charge. The Uber service charges a one-time fee of $5, which leaves Fred with $15 for the per-mile charges.
Since Uber charges $2.50 per mile, we divide the remaining amount by the per-mile charge:
Total budget after one-time fee = $20 - $5 = $15
Maximum miles = $15 / $2.50 per mile = 6 miles
Hence, Fred can afford to take an Uber for a distance of up to 6 miles to his sister's house.