25 SAT Word-Problem Types With Answers

For each word problem, define variables and units before calculating. These compact examples show 25 recurring models; the answer line is intentionally short so you can cover it and solve first.

1. Constant rate: 210 miles in 3.5 hours. Speed? 60 mph.
2. Distance: 48 mph for 2.25 hours. Distance? 108 miles.
3. Start plus rate: 30 setup + 12/month for 5 months. $90.
4. Percent increase: 240 rises 15%. 276.
5. Percent decrease: 85 discounted 20%. **68.**
6. Reverse percent: After a 25% increase, value is 100. Original? (100/1.25) = 80.
7. Successive percent: 10% rise then 10% fall on 200. (200(1.1)(.9)) = 198.
8. Ratio parts: red:blue = 2:7, total 45. Red? (2/9(45)) = 10.
9. Proportion: 5 notebooks cost 18. 15 cost? **54.**
10. Direct variation: (y=kx); y=28 at x=7. k? 4.
11. Inverse variation: (xy=24); x=6. y? 4.
12. Linear model: temperature starts 12° and rises 3°/hour. (T=12+3h); at 5 hours 27°.
13. Break-even system: plans (20+4x) and (8x). Equal when (20=4x): x=5.
14. Mixture total: 3 L at 20% plus 2 L at 50%. Pure amount (0.6+1=1.6) L; concentration (1.6/5) = 32%.
15. Simple interest: 500 at 6% annually for 2 years. (I=Prt\) = **60.**
16. Exponential growth: 400 grows 5% for 2 periods. (400(1.05)^2) = 441.
17. Exponential decay: 800 retains 75% for 2 periods. (800(.75)^2) = 450.
18. Arithmetic sequence: first term 7, common difference 4. Tenth? (7+9(4)) = 43.
19. Weighted mean: 8 scores average 70 and 2 average 90. 74.
20. Median: values 2, 4, 8, 11, 19. 8.
21. Probability: 5 green of 20 equal tokens. 1/4.
22. Conditional probability: 12 of 30 club members are seniors; 5 of those seniors lead teams. Given senior, leader probability? 5/12.
23. Area scale: side lengths double. Area factor? 4.
24. Volume scale: dimensions triple. Volume factor? 27.
25. Unit conversion: 72 kilometers in 2 hours. km/min? (72/120) = 0.6 km/min.

How to review these

For each type, write the model before using a calculator, solve, and state the requested unit. Then change one number and solve again. Memorizing these answers is useless; recognizing the relationship is the skill.

College Board’s SAT Math overview defines the tested domains. Continue with our 12 translation examples, math shortcut guide, and SAT Math practice test.

Types 1–7: rate and percent checks

For constant rate, keep units visible. 210 miles ÷ 3.5 hours produces miles per hour. For distance, multiplying 48 miles/hour × 2.25 hours cancels hours and produces miles.

For percent change, identify the original value before calculating. A 15% increase uses multiplier 1.15; a 20% decrease uses 0.80. Reverse-percent problems divide by the multiplier because the stated number is already the result.

Successive changes multiply. A 10% rise followed by a 10% fall is (1.10(0.90)=0.99), a net 1% decrease—not zero change.

Types 8–14: ratios, models, and systems

For ratio parts, add the ratio numbers to find total parts. A (2:7) ratio has nine parts; with 45 total, each part is 5.

For linear models, distinguish the initial value from the rate. In (T=12+3h), 12 is the starting temperature and 3 is degrees per hour.

Break-even problems set two total-value expressions equal. After solving, check whether the question asks when plans are equal or what the common cost is.

For mixture questions, track the pure amount. Three liters at 20% contains 0.6 liters of the substance; two liters at 50% contains 1.0 liter. Divide total pure amount by total mixture volume.

Types 15–18: growth and sequences

Simple interest (I=Prt) calculates interest, not final balance unless the interest is added to principal. Exponential models apply the same multiplier each period. A 5% growth rate becomes 1.05; retaining 75% becomes 0.75.

For arithmetic sequences, the (n)th term is (a_1+(n-1)d). The tenth term uses nine changes from the first, which is why the example uses (7+9(4)).

Types 19–25: data, probability, scale, and units

Weighted means require totals. Multiply each group mean by its group size, add totals, and divide by the combined count.

For conditional probability, shrink the sample space to the given condition. “Given senior” means only the 12 seniors remain in the denominator.

For similar figures, lengths scale by (k), areas by (k^2), and volumes by (k^3). A side-length factor of 3 produces a volume factor of 27.

For unit conversion, write cancellation explicitly. Two hours is 120 minutes, so 72 km divided by 120 min is 0.6 km/min.

A five-step translation template

1. Asked: write the requested quantity and unit.
2. Let: define variables with units.
3. Relate: state the relationship in words.
4. Solve: use algebra, arithmetic, or Desmos.
5. Interpret: answer the original question in a sentence.

Example: “Asked: months. Let (m) be months. Setup fee plus monthly cost equals total: (30+12m=90). Therefore (m=5) months.”

Turn the list into three practice sets

Set A: recognition

Cover the type names. Read each scenario and name the model before calculating. Recognition is the first skill the test demands.

Set B: translation

Write variables, units, and equations for ten problems but do not solve. Compare setups with the answer explanations. This isolates translation from algebra.

Set C: mixed timed work

Choose 12 types in random order. Solve under a reasonable time limit, then classify every miss as recognition, translation, execution, or interpretation.

Common traps across the 25 types

• dividing percent change by the new value;
• adding percent rates in successive-change problems;
• averaging group averages without weights;
• applying a length scale factor directly to area;
• using the original sample space for conditional probability;
• rounding before the final step;
• ignoring positive or integer restrictions; and
• entering an intermediate quantity instead of the requested answer.

Estimate as a final check

A discount should lower a price. A weighted average must fall between the group means. Positive growth should exceed the starting value. Probability must lie between 0 and 1. Units should match the requested quantity.

Estimation will not replace exact work, but it exposes many wrong models and calculator entries in seconds.