Question

Two cell phone companies have different rate plans. Run fast has monthly charges $8 plus $8 per gig of data. B A & D 's monthly charge is $15 plus $4 per gig of data. Your task is to determine under what circumstances each company has the better pricing.

Answer 1

I am going to take this as which is more cost beneficial within a month.

Run Fast: total monthly = $8 flat monthly free + ($8 per gig) times (gigs used)
g = number of gigs
RF cost = $8 + $8g

BAD cost = $15 + $4g

The question asked for pricing advantages for each company, so lets start with RF. When is RF a better deal than BAD. Well, it is when the total cost of RF is less than BAD.
RF cost<BAD cost
We have the costs in terms of dollars, so we can extrapolate circumstances from that.
8+8g < 15 + 4g
Simple algebra here.
4g<7
g<(7/4)
So, we figured out that if RF is less than BAD, then the amount of gigabytes used has to be less than 7/4.

If we do the same thing, but flip the sign of the equation to make BAD cheaper, then we just get g>(7/4)