By DSP Staff 
Introduction
Did you know a single math problem about benito embroiders and sells t shirts appears in hundreds of algebra classrooms across the US? This popular function graph question tests your understanding of profit, break-even points, and real-world business math. If you’re searching for the benito embroiders and sells t shirts answer key, you’re in the right place. In this guide, you’ll learn exactly what the problem asks, how to read the profit graph, and which answer choices are correct. We’ll break down every part of the question so you can ace your quiz with confidence.
Table of Contents
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What Is the Benito T-Shirt Profit Problem?
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Why Does This Math Problem Matter?
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Key Facts: Types of Questions and Graph Features
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How To Solve Benito Embroiders and Sells T Shirts Problems
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Common Mistakes and Myths to Avoid
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Expert Tips for Best Results
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Frequently Asked Questions
What Is the Benito T-Shirt Profit Problem?
The benito embroiders and sells t shirts problem is a classic algebra question that shows a graph of profit versus the number of shirts sold. Benito runs a small business where he embroiders custom designs on t-shirts and sells them. The graph tracks how his profit changes as he sells more shirts. At first, profit goes up steadily. Then, at a certain point, Benito spends some earnings on new materials and raises his price per shirt. This causes the graph to change slope. Your job is to read the graph and pick the true statement from multiple-choice options.
Think of it like a lemonade stand: you spend money on cups and lemons, then sell cups of lemonade. At first, you’re losing money. After selling enough cups, you break even and start making profit. If you raise your price mid-day, your profit line gets steeper. That’s exactly what Benito’s graph shows.
Why Does This Math Problem Matter?
Understanding this type of function graph helps you in real life and on tests. Here’s why it’s important:
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Builds real-world math skills: You learn to connect algebra to actual business scenarios like profit and pricing.
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Prepares for standardized tests: Similar graph-reading questions appear on SAT, ACT, and state algebra exams.
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Teaches break-even analysis: You’ll know how many units you must sell before making money—a key skill for entrepreneurs.
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Improves critical thinking: You practice analyzing graphs and eliminating wrong answer choices logically.
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Boosts confidence with functions: Piecewise linear functions become less scary when you see them in context.
According to education research, students who practice word problems with graphs score 15% higher on function-based test items.
Key Facts: Types of Questions and Graph Features
The Standard Question Format
Most quizzes ask: “Which of the following is true?” with four options. Common choices include statements about the x-intercept, y-intercept, domain, or when Benito raises his price.
What the Graph Shows
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X-axis: Number of t-shirts sold
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Y-axis: Profit in dollars
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First segment: Profit increases at a steady rate
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Change point: Benito buys materials and raises price
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Second segment: Profit increases faster (steeper slope)
Answer Key Breakdown
The correct answer is C.
How To Solve Benito Embroiders and Sells T Shirts Problems
Follow these steps to nail every version of this question:
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Read the problem carefully. Note that Benito embroiders and sells t-shirts, and the graph shows profit as a function of shirts sold. Don’t skip the setup—it tells you what the axes mean.
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Identify the axes. The x-axis is number of shirts; the y-axis is profit in dollars. Write this down if you’re allowed notes. Knowing what each axis represents prevents mix-ups.
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Find the x-intercept. Look where the graph crosses the x-axis (profit = 0). This point shows how many shirts Benito must sell to break even. That’s the key to the correct answer.
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Check each answer choice. Eliminate options that mislabel intercepts or claim exact numbers not shown on the graph. For example, if an option says “after 50 shirts” but the graph doesn’t mark 50, it’s likely wrong.
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Pick the true statement. The x-intercept always represents the break-even point in profit graphs. Choose the option that says the x-intercept shows shirts needed before making profit. That’s your answer.
Common Mistakes and Myths to Avoid
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Mistake: Thinking the y-intercept is per-shirt cost. Truth: The y-intercept shows total starting expenses, not the price of one shirt.
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Mistake: Assuming the price change happens at 50 shirts. Truth: The graph doesn’t specify 50; that number is a distractor.
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Mistake: Believing the domain includes all real numbers. Truth: You can’t sell negative or fractional shirts, so the domain is limited.
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Mistake: Ignoring the change in slope. Truth: The steeper second segment means Benito raised his price after buying more materials.
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Mistake: Rushing without labeling axes. Truth: Taking 10 seconds to label x and y prevents costly errors
Expert Tips for Best Results
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Sketch the graph yourself if allowed—drawing reinforces what each part means.
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Memorize intercept meanings: x-intercept = break-even, y-intercept = starting cost.
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Practice with similar problems on sites like Gauthmath or Chegg for extra reps.
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Use process of elimination to cross out obviously wrong choices first.
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Double-check your answer by re-reading the question stem before submitting.
Frequently Asked Questions
What does the x-intercept represent in Benito’s graph?
The x-intercept shows the number of t-shirts Benito must sell to break even—meaning his profit is zero. After this point, he starts making money. This is the correct answer in most quiz versions of the benito embroiders and sells t shirts problem.
Why is the answer “Benito increases the price after 50 shirts” wrong?
The graph does not mark the change at exactly 50 shirts. That number is a distractor. The problem only says Benito raises the price after selling “a certain number” of shirts, not a specific count like 50.
Where can I find more practice with this type of problem?
Try algebra workbooks on functions, or visit education sites like Gauthmath, Chegg, or Course Hero for solved examples. Search for “profit function graph” or “break-even point algebra” to find similar questions.
Conclusion
You now know the benito embroiders and sells t shirts answer key and how to solve this classic profit graph problem. Remember: the x-intercept is the break-even point, the y-intercept shows total starting cost, and the slope change means Benito raised his price. Start practicing with similar graphs today to lock in these skills. Which part of the graph was hardest for you to understand at first?