SOLUTION: A $3.00 toll is charged to cross the bridge from Sanibel Island to mainland Florida. A six-month pass, costing $15.00, reduces the toll to $.50. A one-year pass, costing $150, allo

Question 414458: A $3.00 toll is charged to cross the bridge from Sanibel Island to mainland Florida. A six-month pass, costing $15.00, reduces the toll to $.50. A one-year pass, costing $150, allows for free crossings. How many crossings per year does it take, on average, for two six-months passes to be the most economical choice? Assume a constant number of trips per month, Show work and explain answer.
I am not sure what formula to use for this problem. Please Help! :/
Found 2 solutions by josmiceli, stanbon:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = crossings per year it takes, on average, for two six-months passes to be the
most economical choice.
Let = cost per year to make crossings
Assume a constant number of trips per month
-------------------------------------
Without buying any passes:

Buying 2 6-month passes:

Buying a 1-year pass:

-----------------
First I'll set to find intersection

12 crossings per year make
One more crossing, , make

and

So, becomes more economical on the 13th crossing by $2.50
and it still cost less than the 1-year pass for $150

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A $3.00 toll is charged to cross the bridge from Sanibel Island to mainland Florida. A six-month pass, costing $15.00, reduces the toll to $.50. A one-year pass, costing $150, allows for free crossings.
--------------------------
How many crossings per year does it take, on average, for two six-months passes to be the most economical choice?
Assume a constant number of trips per month, Show work and explain answer.
--------
Cost with two 6-month passes = 30 + 0.50x for x crossings in one year.
Cost of unlimited crossings for one year: $150
Cost of x crossings for one year: 3x
-----
Solve for "x":
30+0.5x < 150
0.5x < 120
x < 240 (2 six-month passes cheaper if # of crossings is less than 120)
----
30+0.5x < 3x
2.5x > 30
x > 12
----
So, 2 six-mth passes cheaper if 12 < x < 240
============================================
Cheers,
Stan H.
=============
RELATED QUESTIONS
A $3.00 toll is charged to cross the bridge from Sanibel Island to mainland Florida. A... (answered by stanbon)
the toll to a bridge is $2.50. A three month pass costs $12.00 and reduces the toll to... (answered by macston)
A tour boat makes the round trip from the mainland to a fishing village in 6 hours. If... (answered by ankor@dixie-net.com)
Twenty-six percent of all cars crossing a toll bridge have a commuter sticker. What is... (answered by stanbon)
A discount pass for a bridge cost $30 a month. The toll for the bridge is normally $5,... (answered by josmiceli)
Sergio's internet provider charges its customers $15 per month plus 4¢ per minute of... (answered by ikleyn)
how do I solve this problem by method of addition and substitution: A toll bridge... (answered by Earlsdon)
jenny leaves florida at 8:00 am. Her average speed results in 50 miles per hour. Jim will (answered by checkley77)
At noon, one ship sails north from Castaway Island at 15 knots and another ship sails... (answered by Abbey)