SAT Word Problems: How to Set Them Up, with 8 Worked Examples
Key Takeaways
- College Board says about 30% of SAT Math questions are set in context, so a 44-question Math section has roughly 13 word problems.
- Word problems appear in all four Math domains: Algebra, Advanced Math, Problem-Solving and Data Analysis, and Geometry and Trigonometry.
- Use the same five steps every time: read what is asked, name the unknowns, translate sentence by sentence, match the units, then solve and check against the story.
- Most lost marks come from answering the wrong quantity, mixing units, adding successive percentages and rounding the wrong way on an inequality.
- Practise the set-up rather than the answer: for every miss, write the equation you should have written and redo the question a week later.
Table of Contents
- What counts as a word problem on the SAT?
- How do you set up an SAT word problem?
- Which SAT word problem types come up most often?
- SAT word problem examples with step-by-step solutions
- Example 1: Rate and distance
- Example 2: Percent increase, then decrease
- Example 3: Ratio in a mixture
- Example 4: Linear model
- Example 5: System of two equations
- Example 6: Unit conversion
- Example 7: Inequality with a limit
- Example 8: Exponential growth
- What mistakes cost the most points on SAT word problems?
- How should you practise SAT word problems?
SAT word problems are the Math questions set in a real-world, science or social studies scenario. College Board says approximately 30% of the Math section’s questions are set in context, so on a 44-question section you can expect roughly 13 of them. The maths inside them is rarely harder than in the bare equations. What costs marks is turning the words into the right equation.
This guide gives you one method for setting up any SAT word problem, the types that come up most, and eight worked examples. Every example was written by Galvanize for this page, so none of them is a College Board question.
What counts as a word problem on the SAT?
College Board calls them in-context questions: you “consider a science, social studies, or real-world scenario and apply your math skills and knowledge, along with an understanding of the context, to determine the answer.” They are spread across all four Math content domains rather than kept in one block.
| Math domain | Questions per test | Word problems you will see here |
|---|---|---|
| Algebra | 13–15 | Linear models, systems of two equations, inequalities with a limit |
| Advanced Math | 13–15 | Growth and decay, quadratic models such as area or projectile height |
| Problem-Solving and Data Analysis | 5–7 | Rates, ratios, percentages, unit conversion, reading data |
| Geometry and Trigonometry | 5–7 | Area, volume and similar-triangle problems described in words |
Source: College Board, The Math Section: Overview, checked 28 October 2026. The Math section is 70 minutes in two 35-minute modules with 44 questions in total, according to How the SAT Is Structured. About 75% of Math questions are four-option multiple choice; the rest ask you to enter your own answer, which is common for word problems because there are no options to work backwards from.
How do you set up an SAT word problem?
Use the same five steps every time. They feel slow at first, but they stop the two most common errors: answering a different question from the one asked, and mixing up units.
- Read the last sentence first. It tells you what to find: a number of tickets, a cost in dollars, a time in hours. Write that down before you touch the numbers.
- Name the unknowns. Pick a letter for each quantity you do not know, and write what it stands for, including the unit (for example, s = number of student tickets).
- Translate sentence by sentence. “Total” or “altogether” usually means an equation with a sum; “at most” means ≤; “per” means a rate or a division; “percent of” means multiply by a decimal.
- Make the units match. Convert minutes to hours, millilitres to litres or cents to dollars before you combine quantities.
- Solve, then check against the story. A negative number of people or 25.8 boxes is a signal to reread. Then confirm that your answer is the quantity the last sentence asked for.
Which SAT word problem types come up most often?
| Type | Words that signal it | The set-up |
|---|---|---|
| Rate and distance | per hour, speed, at a constant rate | distance = rate × time |
| Percent change | increased by, discount, then, of the new price | multiply by (1 + rate) or (1 − rate) for each change |
| Ratio and proportion | for every, in the ratio, mixture | total parts, then value of one part |
| Linear model | fixed fee plus, each additional, per unit | y = (starting value) + (rate)x |
| System of equations | two kinds of item, a total count and a total value | one equation for the count, one for the value |
| Unit conversion | in a week, in litres, per second | multiply by conversion factors so units cancel |
| Inequality | at most, no more than, at least, maximum | ≤ or ≥, then round in the direction the story allows |
| Exponential growth or decay | doubles every, decreases by a percent each | start × (factor)number of periods |
SAT word problem examples with step-by-step solutions
Try each one before reading the solution. Time yourself: on test day you have about 95 seconds per Math question on average (70 minutes for 44 questions).
Example 1: Rate and distance
A cyclist rides at 18 kilometres per hour for 40 minutes, then at 24 kilometres per hour for 25 minutes. How many kilometres does she ride in total?
- Find: total distance in kilometres.
- Units: the speeds are per hour, the times are in minutes, so convert. 40 minutes = 40/60 hour; 25 minutes = 25/60 hour.
- First part: 18 × 40/60 = 12 km. Second part: 24 × 25/60 = 10 km.
- Answer: 22 kilometres.
The trap: multiplying 18 by 40 and 24 by 25 gives 1,320, an answer that some test-takers grid without noticing it is impossible for a 65-minute ride.
Example 2: Percent increase, then decrease
A jacket priced at $80 goes up by 20%. The new price is then reduced by 15%. What is the final price?
- Find: final price in dollars.
- Each change multiplies the current price: up 20% is ×1.20, down 15% is ×0.85.
- Final price = 80 × 1.20 × 0.85 = 80 × 1.02 = 81.60.
- Answer: $81.60, which is 2% above the original, not 5%.
The trap: subtracting 15 from 20 and adding 5% to the original. The second change applies to the new price, not to $80.
Example 3: Ratio in a mixture
A drink is made by mixing concentrate and water in the ratio 2 to 7. How many litres of concentrate are needed to make 3.6 litres of drink?
- Find: litres of concentrate.
- Total parts: 2 + 7 = 9. One part: 3.6 ÷ 9 = 0.4 litres.
- Concentrate is 2 parts: 2 × 0.4 = 0.8.
- Answer: 0.8 litres.
The trap: using 2/7 of 3.6. The ratio compares concentrate to water, so the fraction of the whole drink is 2/9.
Example 4: Linear model
A phone plan charges C = 12 + 0.05m dollars per month, where m is the number of minutes used. (a) What does 0.05 represent? (b) How many minutes can a customer use for a bill of $20?
- (a) 0.05 is the slope: the cost in dollars of each additional minute. The 12 is the fixed monthly fee, paid even with zero minutes.
- (b) Set C = 20: 12 + 0.05m = 20, so 0.05m = 8 and m = 8 ÷ 0.05 = 160.
- Answer: 160 minutes.
Questions that ask what a number “represents” are common on the SAT. Name it with its unit: “dollars per minute”, not just “the rate”.
Example 5: System of two equations
A school theatre sold 220 tickets. Adult tickets cost $14 and student tickets cost $9. Ticket sales came to $2,505. How many student tickets were sold?
- Unknowns: a = adult tickets, s = student tickets.
- Count equation: a + s = 220. Value equation: 14a + 9s = 2,505.
- Substitute a = 220 − s: 14(220 − s) + 9s = 2,505, so 3,080 − 5s = 2,505 and s = 115.
- Check: a = 105; 14 × 105 + 9 × 115 = 1,470 + 1,035 = 2,505.
- Answer: 115 student tickets.
The trap: solving correctly for a and reporting 105. Step 1 of the method, reading what the question asks for, prevents it.
Example 6: Unit conversion
A tap leaks 3 millilitres of water every 10 seconds. At this rate, how many litres leak in one week?
- Rate: 3 ÷ 10 = 0.3 millilitres per second.
- Seconds in a week: 60 × 60 × 24 × 7 = 604,800.
- Millilitres: 0.3 × 604,800 = 181,440. Litres: 181,440 ÷ 1,000 = 181.44.
- Answer: 181.44 litres.
Write the units next to every number. If they do not cancel down to litres, a conversion is missing.
Example 7: Inequality with a limit
A delivery van can carry at most 900 kilograms. The driver weighs 75 kilograms and each box weighs 32 kilograms. What is the greatest number of boxes the van can carry with the driver?
- “At most” means ≤: 75 + 32b ≤ 900.
- 32b ≤ 825, so b ≤ 25.78…
- Boxes come in whole numbers and 26 would break the limit, so round down.
- Answer: 25 boxes.
The trap: rounding 25.78 up to 26. With a maximum, you round down; with a minimum (“at least”), you round up.
Example 8: Exponential growth
A bacteria culture starts with 500 cells and doubles every 3 hours. How many cells are there after 12 hours?
- Model: N(t) = 500 × 2t/3, where t is hours.
- 12 hours is 12 ÷ 3 = 4 doubling periods.
- N(12) = 500 × 24 = 500 × 16 = 8,000.
- Answer: 8,000 cells.
The trap: multiplying 500 by 2 four times is right, but multiplying 500 by 2 × 12 (linear thinking) gives 12,000. “Doubles every” always means an exponent.
What mistakes cost the most points on SAT word problems?
- Answering the wrong quantity. Solving for adults when the question asked for students (Example 5) is the most common way to lose a mark you had earned.
- Mixed units. Minutes with hours, millilitres with litres. Convert before you calculate.
- Adding percentages. Successive percent changes multiply; they do not add (Example 2).
- Rounding the wrong way. “At most” rounds down, “at least” rounds up (Example 7).
- Not checking against the story. A negative price or a fractional number of people means the set-up is wrong, not the arithmetic.
How should you practise SAT word problems?
Practise the set-up, not just the answer. For each question you miss, write the equation you should have written, then redo the question a week later without looking.
- Work through topic-wise questions on our SAT math practice page, which is sorted by domain.
- Read how the four domains fit together in our SAT Math domains guide and the Digital SAT exam overview.
- Take a timed SAT practice test and turn your raw score into a scaled score with the SAT score calculator.
Not sure whether word problems or another domain is holding your score back? Start with the free SAT diagnostic test, which shows your weak areas by domain. If you are planning US applications as well, our admission counselling team can help you set a target score for your college list.
Frequently Asked Questions
How many word problems are on the SAT?
College Board says approximately 30% of the Math section’s questions are set in context. The Math section has 44 questions, so expect about 13 word problems across the two Math modules.
Are SAT word problems harder than other Math questions?
Not usually in the maths itself. The extra step is turning the scenario into an equation, which is where most errors happen. Questions in each module still run from easiest to hardest, so a word problem near the end of a module is harder than one near the start.
Which topics do SAT word problems test?
They appear in all four Math domains. The most common are rates and distance, percent change, ratios and mixtures, linear models, systems of two equations, unit conversion, inequalities with a limit, and exponential growth or decay.
What is the best way to set up an SAT word problem?
Read the last sentence first to see what is asked, name each unknown with its unit, translate the scenario one sentence at a time, convert units so they match, then solve and check that the answer makes sense in the story.
Do I have to enter my own answer for SAT word problems?
Sometimes. About 75% of SAT Math questions are four-option multiple choice and the rest are student-produced responses, where you type your answer. Word problems can be either format.
How long should I spend on each SAT word problem?
The Math section gives 70 minutes for 44 questions, which is about 95 seconds per question on average. Easier questions early in a module should take less, which leaves time for the harder ones later.
How do I avoid mistakes with percentages on the SAT?
Treat each percent change as a multiplier. A 20% rise is times 1.20 and a 15% fall is times 0.85, applied one after the other. Adding or subtracting the percentages directly gives the wrong answer.
When should I round up or down in an SAT word problem?
Let the story decide. With a maximum, such as a weight limit, round down so the limit is not broken. With a minimum, such as the number of buses needed, round up so the requirement is met.
How can I tell if a word problem needs a system of equations?
Look for two unknown quantities and two separate facts about them, typically a total count and a total value, such as the number of tickets sold and the money they brought in. Write one equation for each fact.
Are the examples on this page real SAT questions?
No. All eight examples were written by Galvanize for this page to match the question types College Board describes. For official questions, use the full-length practice tests in College Board’s Bluebook app.
How should I practise SAT word problems?
Work topic-wise questions first, then timed mixed sets. For every question you miss, write the correct set-up, note which of the common mistakes caused it, and redo the question a week later without looking at the solution.
