Question

a bike rental cost $2.50 per hour plus a fee for renting a helmet, which is required. the total cost of renting a bike for 2 hours is $13
write an equation for the total cost of renting a bike, y, as a function of the hours, y.

Answer 1

To create an equation for the total cost of renting a bike, we can break down the costs involved:

1. 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 \( 2.50x \).

2. 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.