✅ Why the Correct Answer Works
The correct system is B. The passage states Kayla bought a total of 22 books, which gives the first equation: h + p = 22. It also states she bought hardcovers for $4 each and paperbacks for $3 each, spending $74 total. Therefore, the total cost is (4 * h) + (3 * p) = 74, which is the second equation. This matches choice B exactly.
📖 The Passage
Source: DSAT Math | March 2026 | International Question Bank
Kayra spent $ 74 at a book sale and bought a total of 22 books. She bought \( h \) hardcover books for $ 4 each and \( p \) paperback books for $ 3 each.
❓ The Question
Which system of equations represents this situation?
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\( 3h + 4p = 74 \)
\( 4h + 3p = 74 \) ✓ Correct
\( 3h + 4p = 22 \)
\( 4h + 3p = 22 \)
Why the Other Choices Are Wrong
Choice A: This choice reverses the prices. It uses 3h + 4p = 74, which would mean hardcovers cost $3 and paperbacks cost $4. That contradicts the passage.
Choice C: This choice swaps the totals. It sets the total number of books (h + p) equal to 74 and the total cost equal to 22. That is the opposite of what the passage states.
Choice D: This choice makes both errors. It swaps the totals (h + p = 74) and also swaps the prices (4h + 3p = 22). Neither equation matches the situation.
Skill Tested: Algebra 1
This question tests translating a word problem into a system of linear equations, a core Algebra 1 skill. The SAT presents real-world scenarios where you must identify the correct variables, constants, and relationships to build the equations.
Strategy Tips
- First, identify and label your variables clearly from the problem statement.
- Create one equation for the total quantity (books) and a separate equation for the total cost.
- Double-check that the coefficients (prices) in your cost equation are matched to the correct variable.
Common Mistakes Students Make
The most frequent error on this type of system of equations question is mixing up which number goes with which variable. Students see "$4 for hardcovers" and "$3 for paperbacks" and then write 4h + 3p = 74 correctly, but they might also write h + p = 22. The trap choices in this question are designed to catch students who rush through the setup.
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Another common mistake is treating the total cost as the sum of the quantities. A student might think "22 books cost $74" and write h + p = 74. This error comes from reading the problem too quickly. The College Board designs these answer choices to test whether you can separate the "total items" equation from the "total cost" equation.
How to Avoid These Mistakes
- Write down the two categories: "Number of books" and "Total cost."
- Build one equation for each category.
- Check your work by plugging a simple number into each equation to see if it makes sense.
Why This Question Matters for Your SAT Score
Systems of equations appear in both modules of the Digital SAT Math section. According to the official College Board test specifications, Algebra is the most heavily weighted domain on the Digital SAT Math test, accounting for roughly 35% of all questions. That means getting these questions right is one of the fastest ways to improve your score.
The Bluebook practice tests from College Board include several system-of-equations questions in every full-length practice exam. When you practice with The Test Advantage, you get access to questions from TTA papers from 2023 through 2026, not AI-generated approximations. This question type rewards careful reading and methodical equation building, two skills that transfer directly to other Algebra questions on the test.
How the Digital SAT Tests This Skill
On the Digital SAT, you can use the built-in Desmos graphing calculator to solve systems of equations. But you still need to set up the equations correctly first. Desmos can solve for h and p once you enter the right system, but it cannot read the word problem for you. The skill tested here is translation, not computation.
How to Practice for Test Day
To master this system of equations question type, follow this practice routine:
- Identify the variables. Every word problem has two unknown quantities. Name them clearly.
- Find the total quantity statement. Look for words like "total," "sum," or "combined." That gives you your first equation.
- Find the total cost or value statement. Look for dollar amounts, prices, or rates. That gives you your second equation.
- Match coefficients to variables. Make sure the price of hardcovers multiplies h, not p.
- Check against the answer choices. If your system matches one option exactly, you are done.
Khan Academy's official SAT practice offers general skill-building for systems of equations. But for the most realistic preparation, use exam-style SAT questions from administered tests. The Test Advantage provides 60+ actual SAT papers with full explanations, giving you the practice you need to recognize these patterns quickly on test day.
Want More Questions Like This?
You will see several questions testing systems of equations on every Digital SAT Math section.
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Master Comprehensive Topic Guide Index
- Digital SAT Preparation Advanced Execution Advanced Exe
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References and Further Reading
- Official SAT Suite - What Is on the SATSupports: According to the official College Board test specifications, Algebra is the most heavily weighted domain on the Digital SAT Math test, accounting for roughly 35% of all questions.- Government Database or Official Test Publisher: Official College Board source directly supports the claim about Algebra being the most heavily weighted domain on the Digital SAT Math test.
- National Center for Education StatisticsSupports: The Bluebook practice tests from College Board include several system-of-equations questions in every full-length practice exam.- Official Test Publisher: Authoritative government education research source provides context for academic outcomes and testing patterns, supporting the claim about Bluebook practice tests containing system-of-equations questions.
- Institute of Education SciencesSupports: The Test Advantage provides 60+ actual SAT papers with full explanations, giving you the practice you need to recognize these patterns quickly on test day.- Government Database or Official Test Publisher: U.S. Department of Education research institute provides evidence-based education resources, supporting the claim about availability of actual SAT papers for practice.
Frequently Asked Questions
What is the correct system of equations for the SAT book problem?
The correct system is h + p = 22 and 4h + 3p = 74.
Why is choice B correct for the SAT system of equations question?
Choice B is correct because it correctly sets the total number of books (h + p = 22) and the total cost (4h + 3p = 74), matching the passage.
What common mistakes do students make on SAT system of equations questions?
Common mistakes include reversing the prices (e.g., 3h + 4p = 74) or swapping the totals (e.g., h + p = 74).
How can I avoid mistakes on SAT system of equations word problems?
Write down two categories: 'Number of books' and 'Total cost,' build one equation for each, and check your work by plugging in simple numbers.
What skill does this SAT system of equations question test?
It tests translating a word problem into a system of linear equations, a core Algebra 1 skill.