Question

A parking garage in charges a flat rate of $5.00 for 2 hours or less, and $0.25 per hour for each additional hour.

1. Write an equation to model this relationship.
2. How much do you have pay to park for 10 hours?
3. How many hours will $10 buy?

+ is the last question answer 22hours or 20hours?

Answer 1

1. To model the relationship between the parking hours and the cost, we can use the following equation:

`\displaystyle\sf C(h) = \begin{cases} 5.00, & \text{if } h \leq 2 \\ 5.00 + 0.25(h - 2), & \text{if } h > 2 \end{cases}`

Here,
`\displaystyle\sf C(h)` represents the cost
`\displaystyle\sf C` as a function of the parking hours
`\displaystyle\sf h`.

2. To calculate how much you have to pay for parking for 10 hours, we can substitute
`\displaystyle\sf h = 10` into the equation:

`\displaystyle\sf C(10) = 5.00 + 0.25(10 - 2) = 5.00 + 0.25(8) = 5.00 + 2.00 = 7.00`

Therefore, you would have to pay $7.00 to park for 10 hours.

3. To find out how many hours $10 can buy, we need to solve the equation:

`\displaystyle\sf 10 = 5.00 + 0.25(h - 2)`

Simplifying the equation:

`\displaystyle\sf 10 - 5.00 = 0.25(h - 2)`

`\displaystyle\sf 5.00 = 0.25(h - 2)`

Dividing both sides of the equation by 0.25:

`\displaystyle\sf (5.00)/(0.25) = h - 2`

`\displaystyle\sf 20 = h - 2`

Adding 2 to both sides of the equation:

`\displaystyle\sf h = 20 + 2 = 22`

Therefore, $10 would buy you 22 hours of parking.

To clarify, the answer is 22 hours, not 20 hours.