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= ______________________
BA&D=________________________
2. Use your mathematical skill to solve this system of equations using the substitution method. (Show your work here.)
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?_______________________________________________
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?_______________________________________________
y = 25+10x or y = 10x+25
y = 18 + 15x or y = 15x + 18
Here are you two equations.
to solve by substitution
10x + 25 = 15x + 18 Solve for y and then find x.
1. The equation for the monthly charges for Runfast can be expressed as:
Monthly charges for Runfast = $25 + $10 * x, where x is the amount of data in gigabytes.
The equation for the monthly charges for B A&D can be expressed as:
Monthly charges for B A&D = $18 + $15 * x, where x is the amount of data in gigabytes.
2. To solve this system of equations using the substitution method, we'll equate the two equations and solve for x.
$25 + $10 * x = $18 + $15 * x
Rearrange the equation to isolate x on one side:
$10 * x - $15 * x = $18 - $25
Simplify:
-$5 * x = -$7
Multiply both sides by -1 to switch the signs:
5 * x = 7
Divide both sides by 5:
x = 7/5
So, x = 1.4 gigabytes.
3. Graph the results on the accompanying graph, with the x-axis representing the amount of data in gigabytes and the y-axis representing the monthly charges in dollars. Label one line as "Runfast" and the other line as "B A&D".
4. The lines representing the monthly charges for both companies do not start at the origin because they both have a fixed monthly charge that needs to be accounted for. The $25 monthly charge for Runfast and the $18 monthly charge for B A&D contribute to the y-intercept, which is where the lines intersect the y-axis.
5. The y-intercept represents the starting point for the monthly charge when the amount of data used is zero. For Runfast, the y-intercept is $25, indicating that there is a fixed monthly charge of $25 regardless of the amount of data used. For B A&D, the y-intercept is $18, indicating that there is a fixed monthly charge of $18 regardless of the amount of data used.
6. For customers who don't use much data, Runfast may have the better deal. This conclusion can be drawn by comparing the y-intercepts. Runfast has a lower y-intercept of $25 compared to B A&D's y-intercept of $18, indicating that Runfast has a lower base monthly charge for customers who use minimal data.
7. The plans are the same amount when the lines intersect. From the graph, find the point of intersection, which represents the amount of data where the monthly charges for Runfast and B A&D are equal.
8. For customers who use a lot of data, B A&D may have the better deal. This conclusion can be drawn by comparing the slope of the lines. B A&D has a higher slope of $15 per gigabyte compared to Runfast's slope of $10 per gigabyte. This means that for every additional gigabyte of data used, B A&D has a higher increase in monthly charges, which may result in a better deal for heavy data users.