Question

2. The usual toll charge over the bridge is $1.50. If you purchase a special sticker for $10.50, the charge is only $0.80. At least how many trips over the bridge are needed before the sticker would cost less than the toll charge?

Answer 1

If you spend the $10.50, then every time you cross the bridge,
you pay
(1.50 - 0.80) = $0.70 less than if you had not spent the $10.50.

So you need to cross the bridge (10.50/0.70) = 15 times before the savings
add up to the $10.50 .


Check:

14 crossings without the special sticker cost (14 x 1.5) = $21.00
14 crossings with the special sticker cost (14 x 0.8) = $11.20
Savings after 14 trips = ($21.00 - $11.20) = $9.80
Still have not saved the $10.50 that bought you the cheaper crossings.

15 crossings without the special sticker cost (15 x 1.5) = $22.50
15 crossings with the special sticker cost (15 x 0.8) = $12.00
Savings after 15 trips = ($22.50 - $12.00) = $10.50
15 trips have saved the $10.50 that bought you the cheaper crossings. yay !
You have now broken even.
After this, you're 80¢ farther ahead for every future crossing.

I suspect, however, that this is a monthly deal.
If so, the extra $10.50 for cheaper crossings is a good deal only if you
average crossing the bridge more than about every other day, all month,
or roughly one round trip every 4 days during the whole month.