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.

Let's call the Ameri-Mobile activation fee A, and the Cell-U-Later activation fee B.
Let's call the Ameri-Mobile monthly payment c, and the monthly Cell-U-Later monthly payment d
Let's call n the number of months

The cost of the Ameri-Mobile (in business, that's often called "total cost of ownership) is then:
(a + c * n)
The cost of the plan after n months is the activation fee, plus each monthly payment times the number of months paid
The cost of Cell-U-Later is, similarly:
(b + d * n)

You can even find out how many months you'd need to keep the plan for each plan to be equal (the longer you keep the plan, the better is the Cell-U-Later plan, because the activation fee distributes across a higher number of months), by plugging in numbers and solving this equation for n (but that's a bit more advanced):
a + c*n = b + d* n