Word problems?:(

Question

your cell phone plan has just expired with Company X and you want to switch companies. Below is the information you gathered regarding the plans you are considering: Cingular does not have an initial monthly charge. It chagres .75 cents for every minute. Sprint has an initial monthly charge of $25.75 for providing their services and charges .30 cents for every minute. Verizon charges $55.50 per month and .10 cents for very minute. how do I put all this information into Y=mx+b forum? how do I graph it? And looking at that information when does sprint offer the best deal?   When does Cingular offer the best deal? When does Verizon offer the best deal? 

 

Answer 1

Hi Sally,

Y=mX+b form is the standard way to represent linear relationships between variables like these monthly cell phone plans, which relate the monthly cost of a cell phone to the amount it is used each month. In Y=mX+b form, the X represents the number of minutes the phone was used, the m represents the cost per minute, and the b represents the initial monthly charge (which will be added no matter what value X is). Y represents the total cost of the plan. To compare the costs of each plan, we can look at which plans give the lowest Y-values for different values of X.

Cingular - $.75/minute, with no monthly charge
Y = .75X + 0

Sprint - $.30/minute + $25.75 monthly charge
Y = .30X + 25.75

Verizon - $.10/minute + $55.50 monthly charge

Now that we have these equations, we can use a graphing utility such as WolframAlpha (www.wolframalpha.com) to graph them on the same axis and see which plan is cheapest for different amounts of minutes.

I ran the following command in WolframAlpha:
Graph .75X, .30X+25.75, and .10X+55.50 from X=0 to X=250

http://www.wolframalpha.com/share/clip?f=d41d8cd98f00b204e9800998ecf8427e7kteo54lgm

This allows us to see that Cingular, the plan with no initial cost, is cheapest for small numbers of minutes, but as the number of minutes increases, the plans which charge less per minute will become cheaper. Looking at the graph closely and changing the window size will let us zoom in on the points of intersection to see where one plan becomes cost effective when compared to another. Cingular is the cheapest plan if the number of minutes used per month is less than 57.22, Sprint is cheapest for the range 57.22 to 148.75 minutes. Finally, Verizon is cheapest if the number of minutes used per month is greater than 148.75.

Answer 2

All of these cell phone plans represent linear equations. Therefore they must be put into y=mx+b form where m represents the price per minute of a call & b represents the initial monthly charge. Therefore:

 

Cingular = .75x

Sprint = .30x + 25.75

Verizon = .15x + 55.50

 

x would represent the number of minutes used.