To create an equation for the total cost of renting a bike, we can break down the costs involved:
-
The cost of renting the bike: This costs $2.50 per hour. If we let \( x \) represent the number of hours rented, the cost for the bike is \( 2.50x \).
-
The fixed fee for the helmet: Let's denote the helmet fee as \( h \).
Given that the total cost \( y \) for renting the bike for \( x \) hours is $13 when renting for 2 hours, we can set up the equation as follows:
\[ y = 2.50x + h \]
Substituting \( x = 2 \) and \( y = 13 \) into the equation:
\[ 13 = 2.50(2) + h \]
Now we calculate \( 2.50(2) \):
\[ 2.50(2) = 5.00 \]
Now substitute back into the equation:
\[ 13 = 5.00 + h \]
To find \( h \), subtract 5.00 from both sides:
\[ h = 13 - 5 = 8 \]
Now we have the helmet fee \( h = 8 \).
Thus, the equation for the total cost of renting a bike for \( x \) hours becomes:
\[ y = 2.50x + 8 \]
This equation represents the total cost \( y \) as a function of the number of hours \( x \) rented.