Two cell phone companies have different rate plans. Runfast has monthly charges $25 plus $10 per gig of data. B A &D’s monthly charge is $18 plus 15 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. Don’t worry; I have a series of questions to guide you through the process. Good luck!
1. Determine the equation for the monthly charges for Runfast and B A&D.
Runfast= 25+10x
BA&D= 18+15x
2. Use your mathematical skill to solve this system of equations using the substitution method. (Show your work here.)
(25+10x)-(18+15x)
3. Graph the results on the accompanying graph as a visual aid. Don’t forget to label which line is for which company.
4. Why don’t the lines start at the origin? Because it starts off with a flat rate
5. What is special about each of the y-intercepts?________________________________________
6. Which company has the better deal for customers that don’t us much data? How do you know? ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
7. At what point are the plans the same amount? How do you know? ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
8. Which company has the better deal for customers that use a lot of data? How do you know?
looks like the same as this
http://www.jiskha.com/display.cgi?id=1462291500
To solve the system of equations using the substitution method:
1. Set the equations equal to each other: (25+10x) = (18+15x)
2. Simplify and isolate the variable: 25+10x - 18 - 15x = 0
Combine like terms: -5x + 7 = 0
Subtract 7 from both sides: -5x = -7
Divide by -5: x = 7/5 or 1.4
So, x = 1.4 is the value where both companies have the same monthly charges.
To graph the results on the accompanying graph, you will have two lines representing the monthly charges for each company.
The lines start at different points because they have different initial charges (flat rates) before considering the data usage charges.
The y-intercepts represent the initial charges before considering the data usage. For Runfast, the y-intercept is 25, meaning the initial charge is $25. For BA&D, the y-intercept is 18, meaning the initial charge is $18.
To determine which company has the better deal for customers that don't use much data, compare the y-intercepts. In this case, BA&D has the better deal because the initial charge is lower ($18 compared to Runfast's $25).
At the point where the plans have the same amount, the x-value is 1.4, which means if a customer uses 1.4 gigabytes of data, both plans will have the same monthly charge.
To determine which company has the better deal for customers that use a lot of data, compare the slopes of the lines. In this case, since Runfast has a lower per-gigabyte rate compared to BA&D, Runfast will have the better deal for customers that use a lot of data.