compare two cell phone companies offers to see which is the better deal.
Horizon Cell Phone Company
Vertigo Cell Phone Company
Base rate=$40
Plus every minute costs $0.05
vertigo company
Base rate=$30
Plus every minute costs $0.07
Step 1: Write a linear equation of the form y1=mx+b for the Horizon Cell Phone Company. Graph this equation on the xy-plane and label it as y1. Be sure to include a large enough set of x-values (something like [0,800] would be suitable. Graphing values only from [0,10] would not yield very much information, since most cell phone users talk for more than 10 minutes each month. Also, be sure to include a title on the graph and labels on the x- and y-axes.
Step 2: Write a linear equation of the form y2=mx+b for the Vertigo Cell Phone Company. Graph this equation on the same graph. You will now have two lines on the same graph. These should intersect.
Step 3: Find the point of intersection for y1 and y2 algebraically. Show your work and also plot this point on the graph.
Step 4: Analyze which company offers a cheaper deal on cell phone costs and under what conditions. At what value are they the same?
Step 5: Suppose you talk an average of 200 minutes per month. Which is your best option? What is the difference in price between the two companies' charges for 200 minutes.
Step 1: Write a linear equation of the form y1=mx+b for the Horizon Cell Phone Company.
The base rate for Horizon Cell Phone Company is $40, and every minute costs $0.05. So, the equation for Horizon Cell Phone Company is:
y1 = 0.05x + 40
Step 2: Write a linear equation of the form y2=mx+b for the Vertigo Cell Phone Company.
The base rate for Vertigo Cell Phone Company is $30, and every minute costs $0.07. So, the equation for Vertigo Cell Phone Company is:
y2 = 0.07x + 30
Step 3: Find the point of intersection for y1 and y2 algebraically.
To find the point of intersection, we can set y1 and y2 equal to each other and solve for x:
0.05x + 40 = 0.07x + 30
0.02x = 10
x = 500
So, the point of intersection is (500, y).
To find y, we can substitute the value of x into either equation:
y = 0.05(500) + 40
y = 25 + 40
y = 65
The point of intersection is (500, 65).
Step 4: Analyze which company offers a cheaper deal on cell phone costs and under what conditions. At what value are they the same?
To analyze which company offers a cheaper deal, we can compare the costs for different values of x.
For Horizon Cell Phone Company (y1):
- For 0 minutes (x=0), the cost is $40.
- For 500 minutes (x=500), the cost is $65.
For Vertigo Cell Phone Company (y2):
- For 0 minutes (x=0), the cost is $30.
- For 500 minutes (x=500), the cost is $65.
From the analysis, we can see that both companies have the same cost at 500 minutes per month. Below 500 minutes, Horizon Cell Phone Company is cheaper, and above 500 minutes, Vertigo Cell Phone Company is cheaper.
Step 5: Suppose you talk an average of 200 minutes per month. Which is your best option? What is the difference in price between the two companies' charges for 200 minutes.
To find the cost for 200 minutes:
For Horizon Cell Phone Company (y1):
y1 = 0.05(200) + 40
y1 = 10 + 40
y1 = 50
For Vertigo Cell Phone Company (y2):
y2 = 0.07(200) + 30
y2 = 14 + 30
y2 = 44
For 200 minutes, the cost for Horizon Cell Phone Company is $50, and for Vertigo Cell Phone Company is $44.
Therefore, the best option for you, if you talk an average of 200 minutes per month, would be Vertigo Cell Phone Company. The difference in price between the two companies' charges for 200 minutes is $6.
Step 1: To compare the two cell phone companies' offers, we'll start by graphing their linear equations.
Let's start with the Horizon Cell Phone Company. The base rate is $40, and every minute costs $0.05. We can represent the cost, y1, as a function of the number of minutes used, x, using the equation y1 = 0.05x + 40.
Graph this equation on the xy-plane, using a range of x-values that makes sense for cell phone usage. For example, you could use [0, 800] as the range. Be sure to include a title, labels on the x- and y-axes, and plot the points accurately.
Step 2: Now, let's write the linear equation for the Vertigo Cell Phone Company. The base rate is $30, and every minute costs $0.07. We can represent the cost, y2, as a function of the number of minutes used, x, using the equation y2 = 0.07x + 30.
Graph this equation on the same graph as y1. Make sure to use a different color or pattern to differentiate between the lines. Label this line as y2.
Step 3: To find the point of intersection algebraically, set y1 = y2 and solve for x. In this case, we have 0.05x + 40 = 0.07x + 30. Solving this equation will give us the number of minutes at which the costs of the two companies are equal.
Once you find the value of x, substitute it back into either y1 or y2 to find the corresponding y-value. This will give you the point of intersection on the graph. Plot this point accurately.
Step 4: Now that we have the point of intersection, analyze which company offers the cheaper deal under what conditions. If the point of intersection occurs at a lower x-value (number of minutes), then Horizon Cell Phone Company would be cheaper for lower usage. If the point of intersection occurs at a higher x-value, then Vertigo Cell Phone Company would be cheaper for higher usage. The x-value at the point of intersection represents the number of minutes where both companies offer the same price.
Step 5: To determine the best option for you, let's consider the average number of minutes you talk per month, which is 200 minutes. Find the cost for 200 minutes using each company's equation.
Substitute x = 200 into both y1 and y2 equations to find the corresponding y-values. This will give you the cost for 200 minutes for each company. Compare the costs and identify the cheaper option.
To find the difference in price between the two companies' charges for 200 minutes, subtract the cost for 200 minutes from Horizon Cell Phone Company (y1) from the cost for 200 minutes from Vertigo Cell Phone Company (y2). This will give you the price difference between the two companies.