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Word Problem

A phone company has two different long distance phone plans. Plan A charges a monthly fee of $8.51 plus $0.05 per minute. Plan B charges a monthly fee of $6.15 plus $0.08 per minute.
A) Find a function for each long distance plan treating number of minutes used as the independent variable and cost as the dependent variable
B) Graph each of the two functions on the same cartesian plane
C) Find the number of minutes for which the cost of plan Z equals the cost of plan B. What is the cost of each plan at this number of minutes? Label this point on the graph
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4 Answers

A) 
     P= 8.51 + 0.05M
 
     P B = 6.50 + 0.08m
 
 B) PA = 8.51 Vertical intercept    slope 0.05 , another point on line ( 100, 13.51)
 
     PB =  6.50 Vertical Intercept   Slope 0.08  , another point on the line ( 100, 13.50)
 
  C A = C B= 65 + 0.08 ( 67) = 70.36
   
  C )  8.51 + 0.05 M = 6.50 + 0.08 M
 
        2.01 = 0.03 M
 
      M = 2.01/ 0.03 = 67 Minute
   
      CA  = CB = 8.51+ 0.05 ( 67) = $11.86 
A.) 
 
CostOfPlanAPerMonth(numMin) = 8.51 + 0.05*numMin;
CostOfPlanBPerMonth(numMin) = 6.15 + 0.08*numMin;
 
B.) These are linear equations, y = mx + b form. You just need to draw them out.
 
C.) Find numMin such that CostOfPlanAPerMonth(numMin) = CostOfPlanBPerMonth(numMin)
 
This is equivalent to
 
Find numMin such that 8.51 + 0.05*numMin = 6.15 + 0.08*numMin
 
You simply need to perform operations to this equation in order to isolate numMin.
 
Once you have found numMin, (this is where the lines intersect) you simply need to put a dot there and label it with the values resulting from calculating (numMin, CostOfPlanAPerMonth(numMin)) you can also plug in numMin to the plan b too here, the result will be the same since you solved numMin to make that fact true. 
A)Assuming that the dependent variable is cost per month in dollars per month then the functions would be as follows:
 
Fa = 8.51 + 0.05x.
Fb=6.15 + 0.08x.  
 
where x is the independent variable in number of minutes and the dependent variable measured in dollars per month.
 
B) Both of the equations are linear so graphing the two equations is a matter of finding the x and y intercepts.
 
To find the y-intercept set x to zero. The y-intercepts will be 8.51 and 6.15 respectively. Setting y to zero the x-intercepts will be -1702 and -76.875 respectively. 
 
C)I don't know how to find the cost of an unknown plan Z. I am going to assume the question asks where do plans A and B cost the same. In this case you would set the equations equal to each other and solve for x. This will give you the number of minutes at which the plans cost the same. Next simply plug the number of minutes into one of the equations. This will give you the cost of either plan at this point.
 
8.51 + 0.05x = 6.15 + 0.08x; 2.36 = 0.03x; x = 78 minutes and 40 seconds.
 
The cost will be $12.44
 
The point on the graph will simply be where the two lines intersect.
 
 
Hi Paula;
A phone company has two different long distance phone plans. Plan A charges a monthly fee of $8.51 plus $0.05 per minute. Plan B charges a monthly fee of $6.15 plus $0.08 per minute.
A) Find a function for each long distance plan treating number of minutes used as the independent variable and cost as the dependent variable
 
Plan A...y=0.05x+8.51
x=quantity of minutes, independent variable
y=total cost, variable dependent upon x
Plan B...y=0.08x+6.15

B) Graph each of the two functions on the same cartesian plane
 
Unfortunately, I cannot do that here.  However, I can explain how to do it.
Both equations are in slope-intercept format...
y=mx+b
m is the slope.
b is the y-intercept, value of y when x=0.
Plan A slope intercept, (0,8.51).
Plan B slope intercept, (0,6.15)
You may also want to establish the x-intercepts, value of x when y=0.
Plan A...y=0.05x+8.51
0=0.05x+8.51
-8.51=0.05x
-170.2=x
(-170.2,0)
Plan B...y=0.08x+6.15
0=0.08x+6.15
-6.15=0.08x
-76.875=x
(-76.875,0)
Plot all four points, and draw the appropriate lines.

C) Find the number of minutes for which the cost of plan Z equals the cost of plan B. What is the cost of each plan at this number of minutes? Label this point on the graph
 
Plan A=Plan B
0.05x+8.51=0.08x+6.15
8.51=0.03x+6.15
2.36=0.03x
78.67=x
Let's find the value of y corresponding to this...
Plan A...y=0.05x+8.51
y=[(0.05)(78.67)]+8.51
y=12.44
Let's check this result with the other equation...
Plan B...y=0.08x+6.15
y=[(0.08)(78.67)]+6.15
y=12.44
The lines will meet at (78.67,12.44).