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.
g is gigs of data
R is first company, B is the second
R = 4 g + 10
B = 6 g + 6
cost the same when
10 + 4 g = 6 + 6 g
if more data, R is cheaper (lower slope)
cost1 = 10 + 4g
vs
cost2 = 6 + 6g
Your "task" is to simply solve 6+6g = 10+4g to get the break-even point.
Just graph the two equations as if they were
y = 4x + 10 and y = 6x + 6 to illustrate.
http://www.wolframalpha.com/input/?i=plot+y+%3D+4x+%2B+10,+y+%3D+6x+%2B+6
looks like a "much ado about nothing"
Thanks
Also,
4. (1 pt) Why don’t the lines start at the origin?
5. (1 pt) What is the meaning to each of the y-intercepts?
6. (2 pts) Which company has the better deal for customers that don’t us much data? How do you know? Be sure to include how your response relates to the point of intersection.
7. (2 pts) At what point are the plans the same amount? How do you know?
8. (2 pts) Which company has the better deal for customers that use a lot of data? How do you know? Be sure to include how your response relates to the point of intersection.
please help? I need to know how to use the substitution method to figure out the equation
To determine under what circumstances each company has the better pricing, we can set up equations to represent the cost for each company's rate plans and then compare the costs using algebraic techniques like graphing and solving equations.
Let's start by assigning variables to the unknowns. Let's say the amount of data used per month is represented by "x" (in gigabytes).
For Runfast, the monthly charge is $10 plus $4 per gig of data, so we can represent the cost for Runfast as:
Cost(Runfast) = $10 + $4x
For B A & D, the monthly charge is $6 plus $6 per gig of data, so we can represent the cost for B A & D as:
Cost(B A & D) = $6 + $6x
Now, let's graph these equations to visually compare the costs.
Graphing the equation for Runfast: Cost(Runfast) = $10 + $4x
To graph this equation, you can plot points by substituting different values for x, or you can rewrite the equation to slope-intercept form (y = mx + b), where y represents the cost, m represents the slope, and b represents the y-intercept.
In this case, rewriting the equation to slope-intercept form gives us: y = $4x + $10.
Graphing the equation for B A & D: Cost(B A & D) = $6 + $6x
Similarly, rewriting this equation to slope-intercept form gives us: y = $6x + $6.
Now, we can plot these two lines on a graph to compare them visually. The x-axis represents the amount of data used (in gigabytes), and the y-axis represents the cost (in dollars). The point where the lines intersect represents the amount of data at which the costs are equal.
After plotting the lines, we can see that the line for Runfast ($4x + $10) has a steeper slope compared to the line for B A & D ($6x + $6). This means that Runfast becomes a better deal when the amount of data used is relatively higher. On the other hand, B A & D becomes a better deal when the amount of data used is relatively lower.
To determine the exact point at which the costs are equal (the break-even point), we can set the two cost equations equal to each other and solve for x:
$4x + $10 = $6x + $6
Simplifying the equation: -$2x = -$4
Dividing both sides by -2: x = 2
So, at 2 gigabytes of data usage, the costs for Runfast and B A & D are equal.