TEAS math word problems: 20 worked examples by type
TEAS math word problems come in about ten types: percents, ratios and proportions, rates, dose-style proportions, unit conversions, equations from sentences, inequalities, multi-step money and fraction problems, averages, and geometry. Each type has one setup that works every time. Below is each type with worked examples, then 10 practice problems with answers and a 7-day drill.
The math is middle- and high-school level. What costs points is the reading: picking the wrong number to divide by, answering a different question than the one asked, or missing a unit. The on-screen calculator does the arithmetic, so the setup is the skill to practise.
How many word problems are on the TEAS math section?
ATI doesn't publish a word-problem count. It publishes the two math content areas and what each covers:
| Math content area | Scored questions | Word problems you'll see there |
|---|---|---|
| Numbers and algebra | 18 | Percents, ratios, rates, proportions, multi-step problems with fractions and decimals, equations and inequalities written in words, estimating |
| Measurement and data | 16 | Unit conversions, perimeter, area and volume in real settings, averages, reading a table or chart to answer a question |
| Total | 34 scored + 4 unscored = 38 | 57 minutes, about 90 seconds a question |
Counts are ATI's for the TEAS Version 7, the current exam. ATI's content outline writes most math objectives as "solve real-world problems" or "apply… to real-world problems", so plan on a word problem in most math questions, not a few. Prep books put the share at more than half; that is their estimate, not ATI's. For the whole section, read how to pass TEAS math; for every formula, the TEAS math formula sheet.
How to solve any TEAS word problem in four steps
- Read the last sentence first. It says what to find and in what unit: "how many hours", "what percent", "how much did she pay in total".
- Write down what you're given, with units. Cross out any number you don't need. TEAS questions add extra facts on purpose.
- Name the type and write its setup. Percent? part = percent × whole. Ratio? Add the parts. Rate? distance = rate × time. Write the equation before you touch the calculator.
- Check the answer against the story. Should it be more or less than what you started with? Is it in the unit asked? Does a whole number make sense (people, tablets, cans of paint)?
Step 4 catches most traps, because the wrong answer choices are usually what you get from a common slip: dividing by the new value, forgetting to subtract, using the diameter for the radius.
Words to math: the translation table
| The words | Math | Example |
|---|---|---|
| is, was, will be, gives, the result is | = | "12 is 3 more than x" → 12 = x + 3 |
| of (with a fraction or percent) | × | "20% of 60" → 0.20 × 60 |
| per, each, for every, a (as in "$4 a pound") | ÷ (a rate) | "90 miles in 2 hours" → 45 miles per hour |
| more than, increased by, sum, total, combined | + | "5 more than a number" → x + 5 |
| less than, fewer than, decreased by, difference | − | "5 less than a number" → x − 5 (order flips) |
| times, twice, triple, product | × | "twice a number" → 2x |
| quotient, divided by, split equally, ratio of | ÷ | "a number split among 4" → x ÷ 4 |
| at least, no less than, minimum | ≥ | "at least 60 minutes" → t ≥ 60 |
| at most, no more than, maximum, up to | ≤ | "no more than $40" → c ≤ 40 |
| what, a number, how many | x | "what number" → x |
The one that trips people most is "less than". "Seven less than a number" is x − 7, not 7 − x: the 7 is taken away from the number.
Percent word problems
Every percent problem is part = percent × whole. Find which two of the three you have. Percent change is (new − old) ÷ old, always divided by the starting value.
1. Part of a whole
A clinic has 250 patients on its list, and 18% are due for a flu shot. How many is that?
Solution: part = 0.18 × 250 = 45 patients.
2. Finding the whole
42 students passed, which is 35% of the class. How many students are in the class?
Solution: 42 = 0.35 × whole, so whole = 42 ÷ 0.35 = 120. Check: the class must be bigger than 42.
3. Percent increase
Rent rises from $1,200 to $1,290 a month. By what percent did it rise?
Solution: (1,290 − 1,200) ÷ 1,200 = 90 ÷ 1,200 = 0.075 = 7.5%. Dividing by 1,290 gives 7.0%, a trap answer.
4. Tax and tip
A meal costs $40 before tax. Tax is 8%, and the tip is 20% of the pre-tax price. What is the total?
Solution: tax = 0.08 × 40 = $3.20; tip = 0.20 × 40 = $8.00; total = 40 + 3.20 + 8 = $51.20.
5. Two discounts in a row
A jacket is $80. It is marked 20% off, and a coupon takes another 10% off the sale price. What do you pay?
Solution: 80 × 0.80 = 64; 64 × 0.90 = $57.60. Adding the discounts to 30% gives $56, the trap answer: the second discount is taken from a smaller price.
Ratio and proportion word problems
A ratio compares parts; to share a total by a ratio, add the parts first. A proportion sets two equal ratios side by side and cross-multiplies. Keep the same unit on the top of both fractions.
6. Sharing a total by a ratio
A unit's nurses and aides are in the ratio 5 : 3. There are 48 staff. How many are nurses?
Solution: 5 + 3 = 8 parts; 48 ÷ 8 = 6 per part; nurses = 5 × 6 = 30. Using 48 × 5/3 is the common slip.
7. Scale drawing
On a map, 1 inch stands for 25 miles. Two towns are 3.5 inches apart. How far apart are they?
Solution: 1/25 = 3.5/x, so x = 3.5 × 25 = 87.5 miles.
8. Best buy by unit price
A 12-ounce bottle costs $3.60 and an 18-ounce bottle costs $4.86. Which costs less per ounce?
Solution: 3.60 ÷ 12 = $0.30 an ounce; 4.86 ÷ 18 = $0.27 an ounce. The 18-ounce bottle is cheaper per ounce.
Rate, time and distance word problems
distance = rate × time. Make the time units match the rate first: 30 minutes is 0.5 hours at a speed in miles per hour.
9. Time from distance and speed
A student drives 135 miles to a testing center at an average of 45 miles per hour. She leaves at 7:40 a.m. When does she arrive?
Solution: time = 135 ÷ 45 = 3 hours; 7:40 + 3 hours = 10:40 a.m.
10. Work done at a steady rate
A printer prints 24 pages a minute. How long does it take to print 300 pages?
Solution: 300 ÷ 24 = 12.5 minutes, or 12 minutes 30 seconds. Read the choices carefully: 12.5 minutes is not 12 minutes 50 seconds.
Dose-style proportion problems
Because the TEAS is a nursing entrance exam, some problems are set in a clinic: an amount per kilogram, a strength per milliliter. The math is a proportion; you don't need any drug knowledge. These are practice numbers for the math, not doses to use.
11. Amount per kilogram
An order is 5 mg for every kilogram of body weight. The patient weighs 30 kg. Tablets are 50 mg each. How many tablets?
Solution: 5 × 30 = 150 mg; 150 ÷ 50 = 3 tablets.
12. Strength per milliliter
A liquid has 25 mg in each mL. How many mL hold 150 mg?
Solution: 25/1 = 150/x, so x = 150 ÷ 25 = 6 mL. Check: more mg needs more mL.
Unit conversion word problems
Multiply by a conversion fraction whose top unit is the one you want and whose bottom unit cancels the one you have. Chain two fractions when there is no direct factor. The full chart is in the TEAS math conversion chart.
13. Metric within a system
A patient should drink 2.5 liters of water a day from 250 mL cups. How many cups?
Solution: 2.5 L = 2,500 mL; 2,500 ÷ 250 = 10 cups.
14. US to metric, two steps
A child is 3 feet 9 inches tall. What is that in centimeters (1 in = 2.54 cm)?
Solution: 3 ft = 36 in, plus 9 = 45 in; 45 × 2.54 = 114.3 cm.
Equation word problems: sentences into algebra
Let x be the thing asked for, write the sentence as an equation using the table above, solve, then check the answer in the words, not just in the equation.
15. A number puzzle
Seven more than three times a number is 31. What is the number?
Solution: 3x + 7 = 31; 3x = 24; x = 8. Check: 3 × 8 + 7 = 31.
16. Ages
Maria is 4 years older than twice her son's age. Maria is 34. How old is her son?
Solution: 2s + 4 = 34; 2s = 30; s = 15.
17. Consecutive numbers
Three consecutive whole numbers add to 81. What are they?
Solution: x + (x + 1) + (x + 2) = 81; 3x + 3 = 81; x = 26. The numbers are 26, 27 and 28.
Inequality word problems
"At most" and "no more than" are ≤; "at least" is ≥. When the answer must be a whole number, round toward the side the sign allows: down for ≤, up for ≥.
18. A budget limit
A phone plan costs $25 a month plus $0.10 a text. To spend no more than $40, how many texts can you send?
Solution: 25 + 0.10t ≤ 40; 0.10t ≤ 15; t ≤ 150 texts.
Multi-step word problems with fractions and money
Write each step on the scratch paper. The trap is taking the second fraction of the whole instead of what's left.
19. A fraction of what's left
A paycheck is $1,800. One third goes to rent, then one quarter of what's left goes to food. How much is left after both?
Solution: rent = 1,800 ÷ 3 = 600; left 1,200; food = 1,200 ÷ 4 = 300; left = $900. Taking a quarter of $1,800 ($450) gives $750, the trap answer.
Geometry word problems: fence, paint and tanks
Decide first what the story measures: around the edge (perimeter), the flat surface (area) or the space inside (volume). Then round up when you buy whole cans or rolls.
20. Area, then round up
A wall is 10 ft wide and 8 ft tall, with a 3 ft by 4 ft window. One quart of paint covers 25 square feet. How many quarts do you buy?
Solution: wall 10 × 8 = 80 sq ft; window 3 × 4 = 12; paint 80 − 12 = 68 sq ft; 68 ÷ 25 = 2.72, so you buy 3 quarts. "2.72" is a trap choice: you can't buy part of a quart.
Two more quick ones of the same type: a 12 ft by 8 ft garden needs a fence around its 2(12 + 8) = 40 feet, which at $4.50 a foot is $180. A tank 2 ft × 3 ft × 1.5 ft holds 9 cubic feet; at about 7.48 gallons a cubic foot, that is about 67.3 gallons.
Average and estimation word problems
A plain mean is total ÷ count. A weighted average multiplies each score by its weight first. Estimation questions want a rounded answer you get without the calculator: round each number, then multiply.
- Weighted average: a course grade is 30% midterm and 70% final. A student scores 80 and 90. Grade = 0.30 × 80 + 0.70 × 90 = 24 + 63 = 87. Averaging 80 and 90 to 85 is the trap.
- Estimate: 19 boxes at $4.95 each cost about 20 × $5 = $100 (exact: $94.05). If the question says "estimate", choose the rounded value.
Want to see which of these types you miss? Take our free TEAS practice test: 15 questions across all four sections, scored against your program's minimum, with the reason for every answer.
10 TEAS math word problems to practice
Our own problems, in the style of the types above. Cover the answers and give yourself 90 seconds each, the section's pace.
- A clinic saw 360 patients last week, and 15% came in for a flu test. How many?
Answer: 54. 0.15 × 360. - A $64 textbook is on sale for $48. What is the percent discount?
Answer: 25%. (64 − 48) ÷ 64 = 16 ÷ 64. - Red and blue marbles are in the ratio 2 : 7, and there are 63 marbles. How many are red?
Answer: 14. 63 ÷ 9 parts = 7; 2 × 7. - One lap of a hospital hallway is 0.6 miles. How many laps make 4.2 miles?
Answer: 7. 4.2 ÷ 0.6. - A car goes 28 miles on a gallon, and gas is $3.50 a gallon. What does a 420-mile trip cost in gas?
Answer: $52.50. 420 ÷ 28 = 15 gallons; 15 × 3.50. - Four less than five times a number is 46. What is the number?
Answer: 10. 5x − 4 = 46. - Two numbers add to 50, and one is 8 more than the other. What are they?
Answer: 21 and 29. x + (x + 8) = 50; 2x = 42. - Shirts cost $12 each plus a $9 shipping fee per order. With at most $75, how many shirts can you order?
Answer: 5. 12s + 9 ≤ 75; s ≤ 5.5, rounded down. - A nursing student is 1.8 meters tall. About how many inches is that (1 in = 2.54 cm)?
Answer: about 70.9 in. 180 cm ÷ 2.54. - A round rug is 8 ft across. What is its area, with π ≈ 3.14?
Answer: 50.24 sq ft. Radius 4; 3.14 × 16.
Got 8 or more right in under 15 minutes? Word problems are not your gap; spend the time on the topics in how to pass TEAS math. For 24 more questions in the full section mix, take the TEAS math practice test.
A 7-day TEAS word problem drill
About 30 minutes a day: 10 minutes reading one type above, 20 minutes doing 8 to 10 problems of that type from any source, timed at 90 seconds each. Write the setup line for every problem, even easy ones.
| Day | Type | Done when you can |
|---|---|---|
| 1 | Translation table, equations from sentences | Write "5 less than twice a number is 9" as 2x − 5 = 9 without looking |
| 2 | Percents: part, whole, change | Say which number is the whole before you divide |
| 3 | Discounts, tax, tip, two steps | Get the two-discount problem right without adding the percents |
| 4 | Ratios, proportions, unit price | Share any total by a ratio in two lines |
| 5 | Rates and dose-style proportions | Match time units before multiplying |
| 6 | Conversions and geometry | Pick perimeter, area or volume from the story, and round up for whole cans |
| 7 | Mixed set of 20, timed at 30 minutes | 16 of 20 right; redo every miss from the setup line |
If your test is further out, fold this drill into the 4-week TEAS study plan; if it is this week, use the one-week TEAS plan and do days 2, 4 and 7 only.
Mistakes that cost points on TEAS word problems
- Dividing by the new value in a percent change. Always divide by where you started.
- Adding percents that are taken one after the other (two discounts, a raise then a cut).
- Using a ratio part as the total. In 5 : 3, the total is 8 parts.
- Mixing units: minutes with hours, inches with feet, mL with L. Convert first.
- Flipping "less than": "7 less than x" is x − 7.
- Answering the middle step: the question asked how much is left, and you picked the amount spent.
- Not rounding the way the story needs: up for cans, rolls and buses; down for how many you can afford.
- Using every number given. One is often there to distract you.
TEAS math word problems FAQ
Are there a lot of word problems on the TEAS math?
Yes. ATI doesn't give a count, but most of its math objectives are written as real-world problems: percents, ratios, rates, conversions and geometry set in a story. Plan on word problems in most of the 34 scored questions.
Can I use a calculator for TEAS word problems?
Yes. A calculator is built into the exam for the math section; you can't bring your own. It does the arithmetic, not the setup, so practise writing the equation first.
Are TEAS word problems about nursing?
Some are set in a clinic or hospital (weights, doses per kilogram, fluids), and many are everyday: shopping, travel, recipes, rent. None needs medical knowledge; the math is a proportion or a percent.
How long should a TEAS word problem take?
About 90 seconds on average: 57 minutes for 38 questions. If you have no setup after 60 seconds, mark it, pick your best guess and move on; there is no penalty for a wrong answer.
What is the hardest type of TEAS word problem?
For most applicants it is multi-step problems: two discounts, a fraction of what's left, or area minus a window. Write each step on scratch paper and check that the answer matches what the last sentence asked.
Sources
- ATI, ATI TEAS exam details (math questions, minutes, content areas, calculator). Read for our format guide, October 2026.
- ATI, ATI TEAS Version 7 content outline: numbers and algebra, measurement and data objectives.
- NIST, Unit conversion: 1 inch = 2.54 cm exactly; 1 cubic foot ≈ 7.48 US gallons.
- OpenStax, Prealgebra 2e, Rice University: a problem-solving strategy for word problems, translating words into equations.
More math guides: how to pass TEAS math, the TEAS math formulas and conversions, the TEAS math practice test, or all guides. To find out whether word problems are your gap, take the free practice test: 15 questions, scored against your program's minimum.