SOLUTION: 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 costs $40.00 and permits crossing the bridge at no additional cost. h

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: 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 costs $40.00 and permits crossing the bridge at no additional cost. h      Log On


   

Question 949550: 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 costs $40.00 and permits crossing the bridge at no additional cost. how many crossing per three month period does it take for the three-month pass to be the best deal?
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!

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.