To set up the equation for the total cost of renting a bike, we can use the information given. The rental cost is $2.50 per hour plus a fixed fee for the helmet.
Let:
- \( y \) = total cost
- \( h \) = number of hours rented
- \( C \) = cost of renting a helmet
The total cost can be represented as: \[ y = 2.50h + C \]
From the problem, we know that when renting for 2 hours, the total cost is $13: \[ 13 = 2.50(2) + C \]
Calculating the bike rental cost for 2 hours: \[ 2.50 \times 2 = 5 \] So the equation becomes: \[ 13 = 5 + C \]
Now, solve for \( C \): \[ C = 13 - 5 \] \[ C = 8 \]
Now we have the cost of renting a helmet, which is $8. We can write the overall equation for the total cost when renting a bike: \[ y = 2.50h + 8 \]
To find the cost of renting a bike for 5 hours, we substitute \( h = 5 \) into the equation: \[ y = 2.50(5) + 8 \] \[ y = 12.50 + 8 \] \[ y = 20.50 \]
Thus, the total cost of renting a bike for 5 hours is $20.50.