Use the table on the right to write and solve an equation to find the number of miles a rental car must be driven for each option to cost the same for one day.

Question

this is the table

                          cost per day             cost per mile

           option a        $25                            $0.45

           option b        $40                            $0.25

 

URGENT 

Answer 1

Total cost for each car = cost per day + miles*cost per mile

 

option a cost:   25 + 0.45*m     (m=miles)

option b cost:   45 + 0.25*m

 

For the costs to be equal, we just set option a cost = option b cost

 

25 + 0.45*m  =  45 + 0.25*m

 

solve for m:    

0.45*m - 0.25*m = 45 - 25

0.20*m = 20

m = 100         so driving each car for 100 miles should be the same cost, let's check our answer

 

option a:   $25 + 0.45*100 =  $25 + $45 = $70

option b:   $45 + 0.25*100 =  $45 + $25 = $70

 

the equations for option a, b can be thought of as equation for a line

option a:   slope is 0.45  and a Y intercept = 25

option b:   slope is 0.25  and a Y intercept = 45 

the point where these lines intersect (are =) is the solution, miles = 100.