Word Problem Translation on the SAT
Turn Words into Equations
Build equations from context, spot patterns fast, and practice with intent.
Why the SAT Emphasizes Word Problem Translation
Word problems are not about fancy math, they are about translation. The SAT uses them to test whether you can identify the quantities, define a variable, and turn words into equations.
This lesson shows a repeatable translation process. You will practice turning phrases into algebra, checking units, and avoiding the classic mistake of reversing comparisons like "three less than".
A Simple Definition Unlocks Word Problem Translation
Start by choosing a variable that represents the quantity you need. Then translate each part of the sentence into an algebraic expression. Use units to keep yourself honest.
Phrases like "less than" and "fewer than" reverse the order of subtraction. Write the full statement in words first, then convert it to math to avoid flipping the terms.
Work Through Word Problem Translation Step by Step
Translate and solve: A number plus $7$ equals $3$ times the number.
Translate: A number increased by $7$ is $3$ times the number.
Let the number be $x$
Solve for $x$ to isolate the variable.
Divide both sides by the coefficient to isolate the variable.
Use Desmos to Check Word Problem Translation
Translate and solve: A number plus $7$ equals $3$ times the number.
Desmos can check your equation by graphing both sides and finding the intersection. It is useful if the translation leads to messy arithmetic.
y = x + 7
y = 3x
Translation is the real skill here. Desmos helps after the equation is built.
Desmos is faster after the equation is set up, because you can solve or graph quickly. Algebra is faster for the translation step itself, since Desmos cannot interpret the words for you.
Expert move: After you translate the problem, graph left and right sides or test candidate values quickly in Desmos; keep only values that fit the context.
When to skip Desmos: If a quick algebra step or estimation settles it, solve by hand and use Desmos only to verify.
- Desmos features used: graphing, intersections.
- Common mistake: reversing subtraction in phrases like "5 less than a number".
Practice Word Problem Translation with SAT-Style Questions
Translate each sentence into an equation or solve it.
Translate: Five more than twice a number is .
A number decreased by is . What is the number?
A movie ticket costs plus service fee. If the total is , how many tickets were bought?
Translate: The sum of a number and is less than .
Key Takeaways to Remember for Word Problem Translation
- Define a variable, then build the equation from relationships.
- Watch for reversal with "less than" phrases.
- Desmos helps check after the equation is built.
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