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A guide gives dogsled tours during the winter months. The guide charges one amount for the first hour of a tour and a different amount for each hour after the first. You paid \$55 for a 2 hour dogsled tour. Your friend paid \$70 for a 3 hour tour.

a. Explain why this situation can be modeled by a linear equation.

b. Write an equation that gives the cost (in dollars) of a dogsled tour as a function of the number of hours after the first hour of the tour.

Apr 3, 2018

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a )

Let the cost for the frst hour  =  M

Let the cost for each  hour after that be  N

So....  the cost you paid can be modeled as

M + 1N  = 55

The cost your friend paid  is

M + 2N  = 70

Both of these are linear  because  we have equations in two variables that will result in straight lines when  plotted on a graph

If we subtract the first equation from the second we get

N  = \$15......so....this must be the cost per hour after the first hour

Then  the cost for the first hour  is just     M +  15  =  55  ⇒   M  = \$40

b) So....to express the total cost of a tour, C, we have

C  =  40  + 15N       whwere N is the number of hours after the first one

Apr 3, 2018