A toll to a bridge is 300 a 3 month pass cost 750 and the...

A toll to a bridge is $3.00. A 3 month pass cost $7.50 and the toll is reduced to $0.50. A 6 month pass costs $30 and permits crossing the bridge for no addition fee. 1) find the equation for the cost of a 3 month pass for x amount of crossings 2) find the equation for the cost of a 6 month pass for x amount of crossings 3) how many crossings per 3 month period does it take for the 3 month pass to be the best deal... set up inequality and solve for x... 2 parts

Transcript

00:01 So in this question, we have a bridge that requires some toll to cross.

00:05 So if we don't have any pass, it requires us three per crossing.

00:10 But if we have a three month pass, the pass costs us 7 .5 and it costs us an additional fee of 0 .5 for crossing.

00:19 However, if we have a six month pass, we just need to buy the pass for 30 and then there is no additional fee for crossing the bridge.

00:27 So in part a, we have to find the cost function of the three month pass.

00:30 Past.

00:31 That is that if we have the number of crossing, we need to know how much does it cost if we have a three month pass in total.

00:38 So i'm defining the cost function as a c of x, where x is the number of crossings.

00:46 So first let's write the base fee that is 7 .5.

00:52 That is going to, that we have to pay in any case if we are crossing the bridge for one time or 20 times, no matter how many times we are crossing the bridge right then there is the fee that we have to pay every time we cross the bridge and that is 0 .5 and we can simply multiply this by x that is the number of time we cross the bridge and this is our cost function for a three -month pass now the cost function for a six month pass is well we have 30 for the cost of the pass and then we have no additional fee for crossing the bridge so this is pretty much all we need to do for for to find the cost function of a six month pass.

01:35 Now in part c, the question requires us to find the number of crossings it would take for the three month pass to become the best deal.

01:45 So we have to look at two scenarios here.

01:48 In the first scenario, we have to compare the three month pass with the no pass situation and then we have to compare the three month pass with the six month pass and see how many crossings does it take for the three month pass.

02:04 To remain the most cost -effective one.

02:08 So let's find out the cost function of the no -pass situation...

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