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.
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