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
Oct 4, 2015

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

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+2X = 5+3X#,
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.