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21 votes
21 votes
The toll to a bridge is 2.50. A three-month pass costs $12.00 and reduces the toll to $0.50. A six month pass $37 and permits crossing the bridge for no additional fee. How many crossing per three month period does it take for the three month pass to be the best deal.

User Hiadore
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1 Answer

14 votes
14 votes

c=number of crossings; Q=quarterly pass; S=semi-annual pass; P=pay as you go

P=$2.50c

Q=$12+$0.50c

S=$40

Compare single pay and quarterly ticket:

$2.50c=$12+$0.50c Subtract $0.50c from each side

$2.00c=$12 Divide each side by $2.

c=6 6 crossings is the break even for single pay and quarterly ticket: more crossings favor the ticket.

Compare quarterly and semi-annual tickets:

3 month pro-rated cost of semi annual ticket=$20

$20=$12+$0.50c Subtract 12 from each side

$8=$0.50c Divide each side by $0.50

16=c The break=even point between quarterly and semi annual tickets is 16 crossings per 3 months. More than this favors the semi annual ticket.

ANSWER: The three month pass is the best deal if you cross between 6 and 16 times during the three month period.

I hope this help you

User Martin Cazares
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