Question

Ismael is comparing cell phone plans before upgrading his phone. Ameri-Mobile offers a low activation fee, but a high monthly payment. Cell-U-Later offers a lower monthly rate, but the activation fee is higher. Create a possible algebraic expression for both Ameri-Mobile and Cell-U-Later that shows the amount paid after an unknown amount of months have passed. Justify how you created those expressions and identify what each term and factor represents in terms of the cell phone plans.

Answer 1

You know, this will be my 1,000th question answered as of now? :)
Any ideas how to approach this problem?

Answer 2

1,000TH? WOW . Lmaoo that's a lot. and Nope no idea lmao

Answer 3

k.

Let A = Ameri-Mobiles fees and monthly payment
Let C = Cell-U-Later fees and monthly payment

We want C's monthly fee to be lower than A's
We want C's activation fee to be higher than As

let m be the number of months that have passed

Let's make up some numbers

C monthly fee = 10
A monthly fee = 20
C activation fee = 100
A activation fee = 50

After m months, C will cost 10m+100
After m months A will cost 20m+ 50

Do you see what we've done so far?

Answer 4

Yes , I actually do
lol

Answer 5

nice, so lets compare C to A after m months:

Is 10m + 100 > 20m + 50?

Just take anything for m. Say m = 1, for example. Is this inequality true?

Answer 6

Just plug in m=1 into this inequality:

10(1) + 100 > 20(1) + 50

is this true?

110 > 70?

If so, then Plan C is more expensive than Plan A at 1 month. Does Plan C ever get less expensive than plan A?

Answer 7

So far, are you okay with this?

Answer 8

Uhm ,kind of .. a little kinda catching on

Answer 9

I'm taking the equation 10m + 100 to represent the cost of Plan C (Cell-U-Later) and 20m + 50 to represent the cost of Plan A (Ameri-Mobiles). However, since Plan A has a higher monthly fee, you would expect that at some point, Plan C would become less expensive. I'm asking, when does this happen?

It happens when 10m + 100 < 20m + 50.

If you understand this, we can find out when Plan A becomes more expensive than Plan C.

10m - 20m < 50 - 100
-30m < -75
30m > 75
m > 75/30= 2.5 months

So after 2.5 months, Plan C is cheaper than Plan A

Answer 10

Okay.

Answer 11

I know this is challenging. But just keep trying, you'll get it. I promise. :)

Answer 12

Lol alright thank you :)