Rita will rent a car for the weekend. she can choose one of two plans. the first plan has no initial fee but costs $0.90 per mile driven. the second plan has an initial fee of $60 and costs an additional $0.40 per mile driven. how many miles would rita need to drive for the two plans to cost the same?

Let M = #miles driven

Plan 1:   .50M + 70  = total cost

Plan 2    .70M = total cost

To know how far she would drive to have an equal cost for either plan just set the equations equal to each other

.70M = .50M + 70

subtract .50M from both sides

.20M = 70

M = 70/.20 = 350 miles

Check the answser:

Plan 1:  .50(350) + 70 = 175 + 70 = $245

Plan 2:  .7(350) = $245

they are equal so our answer checks as correct