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.
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)
To determine under what circumstances each company has the better pricing, we need to compare the total charges of both companies based on the amount of data used.
Let's say x represents the amount of data used in gigabytes (GB).
For Run Fast:
The monthly charge is $8, and the cost per gig of data is $8. So the total charges for Run Fast would be:
Total Charges for Run Fast = $8 + ($8 * x)
For B A & D:
The monthly charge is $15, and the cost per gig of data is $4. So the total charges for B A & D would be:
Total Charges for B A & D = $15 + ($4 * x)
Now, we can compare the total charges of both companies.
If we set the total charges for Run Fast equal to the total charges for B A & D, we can determine the break-even point.
$8 + ($8 * x) = $15 + ($4 * x)
Simplifying this equation, we can find the break-even point:
$8x - $4x = $15 - $8
$4x = $7
x = $7 / $4
x = 1.75
So, when the amount of data used (x) is less than 1.75 GB, Run Fast has the better pricing. If the amount of data used is greater than 1.75 GB, B A & D has the better pricing.
Therefore, Run Fast is more cost-effective for data usage below 1.75 GB, while B A & D becomes more cost-effective for data usage exceeding 1.75 GB.