Question

Can I have some help with this please? Not quite sure how to solve it.


Kareem will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $61.98 and costs an additional $0.07 per mile driven. The second plan has an initial fee of $53.98 and costs an additional $0.12 per mile driven. How many miles would Kareem need to drive for the two plans to cost the same?

Answer 1

so lets say he drives m miles in each plan, how much would it cost him in each case?

Answer 2

@DanHowell

Answer 3

The first plan would be $61. 98 and the second would be $53.98, if that what you mean.

Answer 4

not exactly, so for e.g. the first plan would cost him 61.98 + 0.07m do you see why?

Answer 5

He pays the initial fee, and then the extra cost per mile, as he does "m" miles

Answer 6

yeah, I see why, so the second would be 53.98 + the $0.12.

Answer 7

yup but you forgot the m, so its 53.98 + 0.12m

Answer 8

now what we can do is let the first case = the second case so that we can solve for m

Answer 9

does that make sense?

Answer 10

Not exactly..? Do you mean like plug them into each other?

Answer 11

no I meant that because we have worked out the total costs for both plans, we can now let these costs equal each other and solve for m (because the question is asking us to find the miles driven for both plans to cost the same)

Answer 12

ohhh understood, sorry. Alrighty, what first?

Answer 13

no problemmmm so first write up an equation in which cost 1 = cost 2

Answer 14

remember cost 1 = 61.98 + 0.07m and cost 2 = 53.98 + 0.12m

Answer 15

I honestly do not have any idea how to do that, I feel like I'm making this waaaay too complicated sorry. Thanks for your help but I think I'm gonna try something else.

Answer 16

wait don't worry about it, its all good! what I meant is just let 61.98 + 0.07m = 53.98 + 0.12m

Answer 17

and now we can collect like terms and solve for m