Question

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.

Answer 1

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