Word problems are the #1 source of stress for SAT test-takers. But here's the secret: the math itself is usually straightforward. The hard part is setting up the equation. Once you have the equation, you already know how to solve it.
The Translation Method
Think of yourself as a translator converting English to math:
| English | Math |
|---|---|
| is, was, equals | |
| more than, increased by | |
| less than, decreased by | |
| times, of, each | |
| per, divided by, ratio | |
| a number, some quantity | (variable) |
Step-by-Step Approach
- Read the whole problem — don't start writing until you understand the scenario
- Define your variable — write down what represents
- Translate phrase by phrase — convert each piece of the sentence
- Solve and check — does your answer make sense in context?
Worked Examples
Example 1: "Five more than three times a number is 23. What is the number?"
Let = the number.
Example 2: "Sarah earns 15 per hour tutoring. Last week she worked a total of 30 hours and earned $396. How many hours did she spend tutoring?"
Let = tutoring hours. Then job hours = .
Sarah tutored for 12 hours.
Example 3: "A store is selling all items at 20% off. If the sale price of a jacket is $56, what was the original price?"
Let = original price. A 20% discount means the customer pays 80%.
The original price was $70.
Common Traps on the SAT
Trap 1: "Less than" reverses the order.
"7 less than " → (NOT )
Trap 2: The question asks for something different than what you solved for.
If you find but the question asks for , the answer is .
Trap 3: Unit mismatches.
If the problem mixes hours and minutes, or feet and inches, convert to the same unit first.
Age Problems
Example 4: "Tom is 4 years older than twice Maria's age. If Tom is 30, how old is Maria?"
Let = Maria's age.
Practice Problems
Problem 1: The sum of three consecutive integers is 72. What is the largest?
Solution
Let the integers be , , .
Largest:
Problem 2: A phone plan costs 0.05 per text. If last month's bill was $52.50, how many texts were sent?
Solution
texts
Problem 3: Twice a number decreased by 9 is equal to the number increased by 6. Find the number.
Solution
Key Takeaways
- Define your variable first — write it down
- Translate phrase by phrase using the conversion table
- Watch out for "less than" (it reverses order)
- Always re-read the question to make sure you're answering what was asked
- Check: plug your answer back into the original word problem
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