Question

Mary will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $55.96 and costs an additional $0.14per mile driven. The second plan has an initial fee of $65.96 and costs an additional $0.12 per mile driven. How many miles would Mary need to drive for the two plans to cost the same?

Answer 1

@kcbunny

Answer 2

She would need to drive 500 miles for the two plants to cost the same

Answer 3

I guess this is because...

Answer 4

There is a $10 difference between the initial fees

Answer 5

And a 2 cents difference between additional miles driven

Answer 6

Thanks! do you know how to do this one? There are 240 pounds on the left plate of a scale and 90 pounds on the right plate. Suppose that you must balance the scale by removing 8-pound bags from the left plate and exactly the same number of 3-pound bags from the right plate. How many bags must you remove from each side in order to balance the scale?

Answer 7

Are you familiar with how to solve two variable equations?

Answer 8

yes.

Answer 9

Actually, I'm not sure you need it. Hang on. Sorry

Answer 10

@justin12lo, if you are still here and want to help with this, that's fine. I know there is a really easy way to figure this out but right now I'm stuck on just subtracting 80 from one side and adding 30 to the other until they are even

Answer 11

8 and 3* sorry

Answer 12

Ok

Answer 13

I'm stuck, the only way I see it is by removing all the bags. It's confusing me at the moment :(

Answer 14

Glad to see we are in the same boat. We'll get this @ashleynicolee :)

Answer 15

There can't be nothing

Answer 16

haha thanks guys

Answer 17

I think it's going to be a matter of finding a common factor. Really you have 0 on one plate and 150 on the other

Answer 18

I'll come back in a few minutes if I have a solution

Answer 19

Okay.

Answer 20

Otherwise I will keep trying

Answer 21

could it be possible you just have to remove all the bags?

Answer 22

That's what I was thinking at first...

Answer 23

I don't know if there is a trick or something or it really is remove every bag.

Answer 24

seems odd that you would have to do that. I suppose it is possible, but what if there aren't any bags on the 90 pound side and thats just the weight of the scale?

Answer 25

i tried that. and its wrong :/

Answer 26

I'm calling my dad. He has a Masters in math so I'll just ask him

Answer 27

well thats extremely helpful!

Answer 28

okay!! I knew there was a super simple way. Okay, so you set it up in an equation.

Because you want both sides equal, they are set equal to each other:
Left side = right side

At the beginning of the problem, we have 240 on one side and 90 on the other:
240 = 90 (I know it really doesn't, but bear with me as I set it up)

Next step is that we are removing 8 pounds from the left side and 3 pounds from the right:
240 - 8 = 90 - 3

Then we know that you have to remove the same number of bags (let x stand for the number of bags) from both sides and that number is multiplied by the number of pounds:
240 - 8x = 90 - 3x

Solve for x

Answer 29

so the answer is 30

Answer 30

Yes. You have to remove 30 bags which is actually all of them.

Answer 31

I totally misread the question the first time and thought we were adding 3 pounds on the right side while taking off 8 on the left.