Word Problems Leading to Linear Equations — Part 2
Master the art of translating real-world scenarios into solvable algebraic equations. This lesson covers every major problem type tested on the SAT — from age puzzles to mixture problems — with a systematic, repeatable process you can use on test day.
1. What Are Word Problems?
Word problems are mathematical problems presented in everyday language. They require you to:
- 1 Comprehend the scenario described in words
- 2 Translate the words into algebraic equations
- 3 Solve the equation using algebra
- 4 Verify the answer makes sense in context
SAT Tip
Word problems make up roughly 30–40% of SAT Math questions. Mastering the translation process is the single biggest score booster for most students.
2. The 7-Step Problem-Solving Process
Use this systematic approach for every word problem. Consistency eliminates careless errors.
Read the entire problem at least twice. Understand what is being asked. Identify all given information. Circle or underline key data.
Clearly state what the variable represents, including units.
Example: "Let $x$ = number of adult tickets sold."
Find how quantities relate. Look for key words that indicate operations (see translation table below).
Translate the relationships into a mathematical equation using your defined variables.
Use algebraic techniques — combine like terms, isolate the variable, simplify.
Substitute back into the original problem (not just the equation). Include units. Answer the actual question asked.