Two cell phone companies have different rate plans. Runfast has monthly charges $10 plus $4 per gig of data. B A &D’s monthly charge is $6 plus $6 per gig of data. Your task, is to determine under what circumstances each company has the better pricing. You will derive and solve a set of equations, graph those equations, and evaluate the meanings for these events.
(1pt) Determine the equation for the monthly charges for Runfast and B A&D.
Runfast = 4g+10
BA&D = 6g+6
(4 pts)Use your mathematical skill to solve this system of equations using the substitution method, not just picking numbers to see what fits. (show your work here)
I already got the first one, I just don't know how to do the second, please help!
so you want to solve
6g + 6 = 4g + 10
2g = 4
g = 2
So at 2 G, the cost is the same for both, namely $18
Where did the 2 come from?
Oh nevermind, thanks for the help!
To solve the system of equations using the substitution method, we need to set the two equations equal to each other and solve for the value of 'g' (the amount of data used) when the monthly charges are equal for both companies.
Setting Runfast equal to BA&D, we have:
4g + 10 = 6g + 6
Now, we can isolate 'g' by moving the similar terms to one side:
4g - 6g = 6 - 10
-2g = -4
Next, divide both sides by -2 to solve for 'g':
g = (-4)/(-2)
g = 2
So, when the monthly charges are equal for both companies (Runfast = BA&D), the amount of data used is 2 gigabytes.
Now we can determine under which circumstances each company has the better pricing by comparing the monthly charges for different amounts of data used.
For Runfast:
Monthly charges for Runfast = 4g + 10
For BA&D:
Monthly charges for BA&D = 6g + 6
To compare the pricing, we can substitute the value of 'g' we found (g = 2) into the equations.
For Runfast:
Monthly charges for Runfast = 4(2) + 10 = 8 + 10 = 18
For BA&D:
Monthly charges for BA&D = 6(2) + 6 = 12 + 6 = 18
We can see that both companies have the same monthly charge of $18 when 2 gigabytes of data is used. So, under the circumstance of using 2 gigabytes of data, both companies have equal pricing.
To further analyze the pricing, we can compare the monthly charges for other amounts of data used. By plugging in different values for 'g' in the equations, we can create a table or plot a graph to visually see which company has the better pricing for different data usage scenarios.