SAT Math Word Problems: 12 High-Frequency Types to Practice

SAT Math word problems repeat a manageable set of relationships. Learn the structure, not the story. Define variables and units, translate one relationship, solve, and answer the requested quantity.

College Board’s SAT Math overview identifies the current domains where these contexts appear.

1. Percent increase/decrease

A price rises from 80 to 92. Percent increase = ((92-80)/80=15%). Divide by the original value.

2. Reverse percentage

After a 20% discount, a price is $72. Original = (72/0.80=90). Adding 20% to 72 uses the wrong base.

3. Constant rate

A machine produces 420 parts in 7 hours. Rate = 60 per hour; in 12 hours it produces 720.

4. Distance-rate-time

A car travels 150 miles at 50 mph. Time = (150/50=3) hours. Track units.

5. Linear cost model

A service charges 25 plus 8 per hour: (C=25+8h). The intercept is initial fee; slope is dollars per hour.

6. Ticket systems

Adult tickets are 12, students 8; 30 tickets total $300. (a+s=30), (12a+8s=300), giving 15 each.

7. Exponential growth/decay

A population starts at 500 and grows 6% yearly: (P=500(1.06)^t). A 6% decay uses 0.94.

8. Weighted average

Eight scores average 70; two scores average 90. Total = (8(70)+2(90)=740); combined average = 74. Do not average group means directly.

9. Mixture

Ten liters of 30% salt contains 3 liters salt. Add (w) liters water for 20%: (3/(10+w)=0.20), so (w=5).

10. Geometry dimensions

A rectangle has perimeter 50 and length 15. (2(15)+2w=50), so (w=10); area = 150. Do not stop at width if area is requested.

11. Density and units

Density = mass/volume. If mass is 240 grams and volume 80 cubic centimeters, density = 3 g/cm³. Convert units before dividing.

12. Probability/counts

A bag has 5 red, 3 blue, and 2 green marbles. Probability of blue = (3/10). For without-replacement sequences, update totals after each draw.

Translation cue table

Phrase	Likely structure
“per,” “each”	rate or slope
“increased by x%”	multiply by (1+x)
“of”	multiplication
“total number and total cost”	system
“every year by same percent”	exponential
“average”	total/count
“concentration”	amount/total mixture

Our word-problem expectation guide teaches the full workflow.

Practice routine

Complete six mixed types without labels. For each:

1. write requested quantity;
2. define variable/unit;
3. write relationship before numbers;
4. solve;
5. estimate and interpret.

Review whether the error came from translation, algebra, calculation, or final interpretation.

Use our 12 translation examples and confidence guide for more sets.

Common traps

• wrong percent base;
• incompatible units;
• linear model for percent growth;
• wrong coordinate from a system;
• early rounding;
• ignoring integer/positive domain; and
• answering an intermediate quantity.

Mini practice set

1. Reverse percent: A jacket's price after a 15% increase is $92. What was the original price?
Let original price be (p). Then (1.15p=92), so (p=80).

2. Linear model: A rental costs 18 plus 6 per hour. If the bill is 60, how many hours were rented? Solve \(18+6h=60\), giving \(h=7\). The 18 is an initial value, not an hourly rate.

3. Weighted average: A class of 12 students averages 78, and a class of 8 averages 88. What is the combined average?
Compute totals: ((12)(78)+(8)(88)=1640). Divide by 20 to get 82.

4. Exponential decay: A 640-milligram sample loses 12% each hour. What remains after 3 hours?
Use (640(0.88)^3), approximately 436.1 milligrams. Subtracting 12% of the original three times would incorrectly model linear decay.

How to create your own mixed drill

Choose six types from the list and remove their headings. Give yourself enough time to write the relationship before calculating. After grading, classify each error as:

• recognition: you chose the wrong model;
• translation: you knew the model but wrote the wrong equation;
• execution: algebra or calculator work failed; or
• interpretation: you solved correctly but answered the wrong quantity.

The categories lead to different fixes. Recognition improves through mixed examples; translation improves by defining variables and units; execution needs targeted algebra; interpretation improves by restating the question after solving.

Estimation as a safety check

Before accepting an answer, predict its direction and rough size. A discounted price should be below the original. A combined average must fall between the group averages. Positive exponential growth should exceed the starting amount. Estimation will not replace exact work, but it catches many setup and entry errors in seconds.

Bottom line

Most SAT word problems are familiar mathematical relationships wearing new contexts. Practice the 12 structures mixed together, keep units visible, and translate the final number back into the question.