# 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?

Oct 4, 2015

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 $X$ hours.
Parking price, according to the first option, will be
$7 + 2 X$
According to the second option, it will be
$5 + 3 X$

Both are linearly dependent on the length of a concert.
If $X = 0$ (concert does not happen) or if $X = 1$ (concert lasts 1 hour) the first option is more expensive. It costs $7 ($0$hours) and$9 ($1$ hour) against, correspondingly, $5 and$8.
For, say, ten and more hours the first option is, obviously, cheaper.

The options are equivalent for some length of a concert if
$7 + 2 X = 5 + 3 X$,
its solution is $X = 2$'
So, for less than $2$ hours concert the second option is better.
For $2$ hours concert options are equivalent.
For greater than 2 hours concert the first option is better.