Question

knowledge check
question 12
tony can choose plan a or plan b for his long distance charges. for each plan, cost (in dollars) depends on minutes used (per month) as shown below.
cost
(in dollars)
minutes used (per month)

Explanation:

Since the problem isn't fully stated (e.g., what's being asked about the two plans, like finding the break - even point, comparing costs for a certain minutes, etc.), we can't provide a solution yet. If we assume the common question is to find the number of minutes where the cost of Plan A equals the cost of Plan B (the break - even point):

Step 1: Determine the equations of the two cost functions

• For Plan B: The cost is a constant. From the graph, when \(x\) (minutes used) varies, \(y\) (cost) is always 22. So the equation for Plan B is \(y = 22\).
• For Plan A: The graph of Plan A is a straight line passing through the origin \((0,0)\) and has a slope. Let's find the slope \(m\). We can take two points, say \((0,0)\) and \((100,10)\) (from the graph, when \(x = 100\), \(y = 10\)). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{10 - 0}{100 - 0}=\frac{1}{10}=0.1\). So the equation of Plan A is \(y=0.1x\) (using the slope - intercept form \(y = mx + b\), and since \(b = 0\) as it passes through the origin).

Step 2: Find the break - even point

To find when the costs are equal, we set the two equations equal to each other:
\(0.1x=22\)
Solve for \(x\):
\(x=\frac{22}{0.1}=220\)

If the question was different, for example, "What is the cost of Plan A when 150 minutes are used?", we would do:

Step 1: Use the equation of Plan A

The equation of Plan A is \(y = 0.1x\). Substitute \(x = 150\) into the equation.
\(y=0.1\times150 = 15\)

Since the actual question is not provided, please clarify what is being asked about the two plans (e.g., find the number of minutes where costs are equal, find the cost for a specific minutes for one of the plans, compare costs for a given minutes, etc.) so that we can provide a more targeted solution.

Answer:

Since the problem isn't fully stated (e.g., what's being asked about the two plans, like finding the break - even point, comparing costs for a certain minutes, etc.), we can't provide a solution yet. If we assume the common question is to find the number of minutes where the cost of Plan A equals the cost of Plan B (the break - even point):

Step 1: Determine the equations of the two cost functions

• For Plan B: The cost is a constant. From the graph, when \(x\) (minutes used) varies, \(y\) (cost) is always 22. So the equation for Plan B is \(y = 22\).
• For Plan A: The graph of Plan A is a straight line passing through the origin \((0,0)\) and has a slope. Let's find the slope \(m\). We can take two points, say \((0,0)\) and \((100,10)\) (from the graph, when \(x = 100\), \(y = 10\)). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{10 - 0}{100 - 0}=\frac{1}{10}=0.1\). So the equation of Plan A is \(y=0.1x\) (using the slope - intercept form \(y = mx + b\), and since \(b = 0\) as it passes through the origin).

Step 2: Find the break - even point

To find when the costs are equal, we set the two equations equal to each other:
\(0.1x=22\)
Solve for \(x\):
\(x=\frac{22}{0.1}=220\)

If the question was different, for example, "What is the cost of Plan A when 150 minutes are used?", we would do:

Step 1: Use the equation of Plan A

The equation of Plan A is \(y = 0.1x\). Substitute \(x = 150\) into the equation.
\(y=0.1\times150 = 15\)

Since the actual question is not provided, please clarify what is being asked about the two plans (e.g., find the number of minutes where costs are equal, find the cost for a specific minutes for one of the plans, compare costs for a given minutes, etc.) so that we can provide a more targeted solution.