Answer: the person can rent the bike for 5.5 hours.
Explanation:
Let x represent the number of hours that a person rents the bike.
Let y represent the total cost of renting the bike for x hours.
A bike shop rents mountain bikes for a $4.00 insurance charge plus $2.50 for each hour. This means that the expression for the total cost of renting the bike for x hours would be
y = 2.5x + 4
Therefore, if a person has $17.75, the number of hours for which he can rent the bike would be
17.75 = 2.5x + 4
2.5x + 4 = 17.75
2.5x = 17.75 - 4
2.5x = 13.75
x = 13.75/2.5
x = 5.5 hours