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

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = crossings per year it takes, on average, for two six-months passes to be the
most economical choice.
Let C = cost per year to make x crossings
Assume a constant number of trips per month
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Without buying any passes:
C%5B1%5D+=+3x
Buying 2 6-month passes:
C%5B2%5D+=+.5x+%2B+2%2A15
Buying a 1-year pass:
C%5B3%5D+=+150
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First I'll set C%5B1%5D+=+C%5B2%5D to find intersection
3x+=+.5x+%2B+2%2A15
3x+=+.5x+%2B+30
2.5x+=+30
x+=+12
12 crossings per year make C%5B1%5D+=+C%5B2%5D
One more crossing, x+=+13, make
C%5B1%5D+=+3%2A13
C%5B1%5D+=+39
and
C%5B2%5D+=+.5%2A13+%2B+30
C%5B2%5D+=+36.5
So, C%5B2%5D 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) About Me  (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.
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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.
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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
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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
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Cheers,
Stan H.
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