To find out how much each parking garage charges, we can set up equations based on the pricing structures provided.
For Garage A:
- Initial fee = $12
- Fee per hour = $5
Thus, the total cost for Garage A,
For Garage B:
- Initial fee = $7
- Fee per hour = $6
Thus, the total cost for Garage B,
Now, we want to find the interval of hours
Substituting the expressions for
Now, we will solve for
- Start by isolating the terms with
on one side: - Simplify:
- Subtract 7 from both sides:
Thus, we can rewrite this as:
This result tells us that Garage A is cheaper than Garage B when
In conclusion:
- The inequalities for the costs are
and . - Garage A is cheaper than Garage B when
hours.