Question

The usual toll charge to use the Bingham tunnel is 50cents, if you purchase a special sticker, the toll is only 35cents, at least, how many trips through the tunnel are needed b4 the sticker cost less than paying for each trip seperately

Answer 1

I think you are missing part of the problem.. How much does the sticker cost?

Answer 2

$5.50,, sorry

Answer 3

OK.. The Bingham tunnel is 50 cents per trip so 1 trip would cost 50 cents, two trips would cost 50 cents times 2 which is $100, 3 trips would cost 50 cents * 3 which is $1.50. So the cost for the Bingham tunnel in general is .50x (x being the number of trips)

With the sticker your cost for 1 trip would be 5.50 + .35 , but for two trips it would be 5.50 + .35 *2, for three trips 5.50 + .35 * 3 so in general this trip with the sticker would cost 5.50 + .35x

So when would 5.50 + .35x < .50x

First thing is to subtract .35 x from both sides
5.50 < .15x
then you would divide both side by .15 and you would get
36.666666 < x if you turn this around you get
x > 36.666666666
SO... when you take the 37th trip and everyone after that (x > 36.66666) it would be cheaper.

to check this out what happens with 36 trips?
.50 * 36 = $18.00
5.50 + .35*36 = $18.10

when you get to the 37th trip
.50 * 37 = $18.50
5.50 + .35 * 37 = $18.45 *** this one is now cheaper