# Armando is comparing parking prices at a local concert, One option is a $7 fee plus $2 per hour. A second option is a $5 entry fee plus $3 per hour. What is the break-even point (intersection) for the two options? Which option do you think is better?

##### 1 Answer

Break even among these two options is 2 hours concert.

For shorter then 2 hours concerts the second option is better,

For longer than 2 hours concerts the first option is better.

#### Explanation:

Assume a concert lasts

Parking price, according to the first option, will be

According to the second option, it will be

Both are linearly dependent on the length of a concert.

If

For, say, ten and more hours the first option is, obviously, cheaper.

The options are equivalent for some length of a concert if

its solution is

So, for less than

For

For greater than 2 hours concert the first option is better.