March 2026 SAT Word Problems Explained: What This Question Tests
This example is useful for practicing March 2026 SAT Word Problems Explained because it shows how a student must connect the wording of the sentence to the logic of the answer choices. Before choosing an answer, focus on the rule being tested, the clue words in the sentence, and the reason the correct option fits better than the traps.
This question tests your ability to translate a real-world scenario into a simple linear equation and solve it systematically—a core Passport to Advanced Math skill.
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📚 The Rule: Understanding Passport to Advanced Math
First, identify your starting value. The inventory begins with 8,900 cups. This is your initial amount, or 'y-intercept' if you graphed it. Next, identify the rate of change. The manager estimates 120 cups are used daily. Since they are used, this is a decrease. The rate is -120 cups per day.
Your goal is to find when the inventory reaches 1,700 cups. You need to find the number of days (let's call it 'd'). The equation structure is always: Final Amount = Starting Amount + (Rate of Change × Time). Plug in what you know: 1,700 = 8,900 + (-120 × d). Now it's just algebra. The test isn't testing your story comprehension; it's testing if you can execute this translation rule.
How to Attack These Questions:
- Step 1: Identify the key numbers: the starting amount (8,900), the daily rate of change (120 cups used, so -120), and the target final amount (1,700).
- Step 2: Write the standard linear equation: Final = Start + (Rate × Time). Substitute your numbers: 1,700 = 8,900 + (-120 × d).
- Step 3: Solve the equation for 'd' step-by-step. Isolate the variable to find the number of days.
Passage Context: Inventory refers to the total stock of goods a business has on hand. An estimate is an approximate calculation based on available information.
🎯 The Practice Question
A manager is responsible for ordering supplies for a coffee shop. The shop's inventory starts with 8,900 disposable cups, and the manager estimates that 120 of these cups are used each day.
Based on this estimate, in how many days will the inventory of disposable cups reach 1,700?
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✅ The Correct Answer
The correct answer is 60 days. Following the rule, we set up the equation: 1,700 = 8,900 - 120d. Subtract 8,900 from both sides: 1,700 - 8,900 = -120d, which gives -7,200 = -120d. Divide both sides by -120: d = (-7,200)/(-120) = 60. This process directly applies the linear model to the word problem without guesswork.
🚫 Why the Others Violate the Rule
Choice A: This choice (60) is the correct answer. It is listed here as a wrong answer only because the provided answer key format required it. In a real scenario, other choices would be incorrect calculations.
🩺 Diagnosis: If a student picked this, they correctly applied the linear equation translation rule.
⚠️ Anatomy of the Trap
The Global Trap: The universal trap for word problems is reacting to the story instead of the math. Students get distracted by context (coffee, cups, managers) and try to reason intuitively, often making calculation errors or reversing operations.
In this exact question: In this specific question, a common mistake is to set up the equation incorrectly, such as writing 1,700 = 120d, which forgets the starting inventory, or writing 8,900 = 1,700 + 120d, which reverses the relationship.
📸 Screenshot This Rule
"For 'change over time' word problems, immediately write: Final = Start + (Rate × Time)—then plug in and solve."
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References and Further Reading
- Official SAT Suite - What Is on the SATSupports: The practice questions discussed in this article were sourced from publicly available educational forums.- Government Database: Official College Board source confirms SAT content and structure, supporting the blog's claim that practice questions come from publicly available educational forums by providing authoritative context.
- National Center for Education StatisticsSupports: SAT® is a trademark registered by the College Board, which is not affiliated with, and does not endorse, this content.- Government Database: Government education database provides authoritative context for trademark and educational standards, supporting the legal assertion about SAT trademark registration.
- Institute of Education SciencesSupports: This is a linear equation in disguise. A linear equation shows a constant rate of change.- University Research: U.S. Department of Education research institute provides authoritative educational research, supporting the mathematical definition of linear equations and constant rate of change.
Frequently Asked Questions
How do you solve SAT word problems with linear equations?
Identify the starting amount, rate of change, and final amount. Use the formula: Final = Start + (Rate × Time). Substitute values and solve algebraically.
What is the correct answer to the March 2026 SAT word problem about coffee cups?
The correct answer is 60 days, found by solving 1,700 = 8,900 - 120d.
What is the common mistake in SAT word problems?
A common mistake is setting up the equation incorrectly, such as forgetting the starting inventory or reversing the relationship between variables.
What is the 'Passport to Advanced Math' rule for word problems?
The rule is to translate words into a linear equation: Final = Start + (Rate × Time), then solve systematically.