Sketch a graph to represent the situation. Label each section. You buy two shirts. The third one is free.
Understand the Problem
The question is asking to create a graph that visually represents a scenario where purchasing two shirts results in getting a third shirt for free. The graph should include labels for each section to clarify the situation.
Answer
The total cost for two shirts is $y = 2C$ and the third shirt is free, leading to points at $(0, 0)$, $(1, C)$, $(2, 2C)$, and $(3, 2C)$.
Answer for screen readers
The graph effectively represents the cost structure with key points labeled at:
- $(0, 0)$: "No shirts bought"
- $(1, C)$: "One shirt bought"
- $(2, 2C)$: "Two shirts bought"
- $(3, 2C)$: "Three shirts (the third is free)"
Steps to Solve
- Identify the Variables
Define the variables in the scenario. Let $x$ be the number of shirts purchased and $y$ be the total cost.
- Define the Cost
Assume the cost of one shirt is $C$. The cost equation for purchasing two shirts, where the third one is free, is:
$$ y = 2C $$
This represents the cost for two shirts.
- Create the Graph
On a graph, plot the number of shirts on the x-axis and total cost on the y-axis.
- For $x = 0$: $y = 0$ (no shirts bought)
- For $x = 1$: $y = C$ (one shirt bought)
- For $x = 2$: $y = 2C$ (two shirts bought)
- For $x = 3$: $y = 2C$ (three shirts, with the third free)
- Label Each Section
Label the following points on the graph:
- Point $(0, 0)$: "No shirts bought"
- Point $(1, C)$: "One shirt bought"
- Point $(2, 2C)$: "Two shirts bought"
- Point $(3, 2C)$: "Three shirts (the third is free)"
- Draw the Line
Connect the points to create a line. The line should be horizontal from the point $(2, 2C)$ to $(3, 2C)$ to represent the free shirt.
The graph effectively represents the cost structure with key points labeled at:
- $(0, 0)$: "No shirts bought"
- $(1, C)$: "One shirt bought"
- $(2, 2C)$: "Two shirts bought"
- $(3, 2C)$: "Three shirts (the third is free)"
More Information
This graph demonstrates a promotional pricing strategy where buying two shirts allows you to receive a third shirt at no extra cost. This type of promotion is common in retail to encourage more purchases.
Tips
- Forgetting to label key points on the graph can lead to confusion.
- Not accurately connecting the points, which could misrepresent the cost when the third shirt is free.
- Assuming the cost of the shirts increases with each additional shirt after two.
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