SAT Math: Setting Up Linear Equations from Word Problems
47+ practice questions in Praczo
The concept, explained
- 1
Always start by defining your variable explicitly — write down what it represents (e.g., "let n = number of notebooks"). The SAT often asks for a related quantity, not x itself.
- 2
Translate key phrases into math: "more than" → +, "less than" → −, "times as many" → ×, "per" → ×, "in total" or "altogether" → =.
- 3
When two quantities together make a total, express both in terms of one variable. If n items are one type and there are 12 total, the other type is (12 − n).
- 4
Write the equation, then re-read the question. It may ask for 2x + 3 or "how many pens," not x directly — solve for x, then compute the answer.
- 5
Check your equation against the problem by substituting your answer back in. Both conditions (total items and total cost) must hold simultaneously.
- ✗ "5 more than x" is x + 5 — but when that expression is on the wrong side of the equation, students flip the subtraction and get the wrong setup.
- ✗ Setting up the cost equation correctly but then answering "how many pens" with the notebooks variable. Always re-read what the question is actually asking for.
SAT-style practice
A store sells notebooks for (3.00 each and pens for )1.50 each. Marco buys a total of 12 items and spends exactly $27.00. Which equation correctly represents this situation, where n is the number of notebooks Marco buys?
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