TEAS Math Word Problems: Types, Strategies, and Worked Examples for Every Category

Here's the uncomfortable truth about TEAS Math: most students don't fail because they can't do the math — they fail because they can't translate word problems into math. The TEAS Math section contains 38 questions, and the majority of them are presented as word problems rather than straightforward computation. If you can decode what a word problem is actually asking, the math itself is usually straightforward arithmetic, algebra, or basic statistics.

This guide dissects every major word problem category on the TEAS, gives you a repeatable strategy for each type, and walks through worked examples so you can see exactly how to approach them on test day.

The Universal Word Problem Strategy

Before diving into specific problem types, internalize this four-step framework that works for virtually every TEAS word problem:

• Step 1 — Read the entire problem twice. On the first read, get the story. On the second read, identify the specific question being asked and underline key numbers and relationships.
• Step 2 — Identify what you're solving for. Write it down. 'Find the total cost' or 'Find how many hours' or 'Find the percentage decrease.' If you can't articulate what you're solving for, you'll wander.
• Step 3 — Set up the equation before calculating. Translate English into math. 'Of' means multiply. 'Per' means divide. 'Is' means equals. 'More than' means addition.
• Step 4 — Check your answer against the context. Does your answer make sense? If the problem asks about a nurse's hourly wage and you got $3,000, something went wrong.

Ratio and Proportion Problems

Ratio and proportion problems are among the most frequently tested word problems on the TEAS. They appear in contexts like medication dosages, recipe scaling, map distances, and staffing ratios. The core skill is setting up equivalent ratios and cross-multiplying.

Example: A hospital maintains a nurse-to-patient ratio of 1:4 on the general floor. If there are 28 patients on the floor, how many nurses are needed? Solution: Set up the proportion: 1 nurse / 4 patients = x nurses / 28 patients. Cross-multiply: 4x = 28. Divide: x = 7 nurses. Always label your units to avoid setting up the proportion incorrectly.

Example: A recipe calls for 2.5 cups of flour for 12 cookies. How much flour is needed for 30 cookies? Solution: Set up: 2.5 cups / 12 cookies = x cups / 30 cookies. Cross-multiply: 12x = 75. Divide: x = 6.25 cups. Notice how the answer is not a round number — the TEAS frequently uses decimal answers to test whether you can work with non-integer values.

Example: On a map, 1 inch represents 15 miles. Two cities are 4.5 inches apart on the map. What is the actual distance? Solution: 1 inch / 15 miles = 4.5 inches / x miles. Cross-multiply: x = 4.5 × 15 = 67.5 miles. Proportion problems are always about finding the missing value in two equivalent ratios.

Percentage Problems

Percentage problems come in three flavors, and recognizing which type you're dealing with is half the battle:

• Finding a percentage of a number: 'What is 15% of 240?' → Multiply: 0.15 × 240 = 36
• Finding what percentage one number is of another: '36 is what percent of 240?' → Divide and multiply by 100: (36 ÷ 240) × 100 = 15%
• Finding the whole when given a percentage: '36 is 15% of what number?' → Divide: 36 ÷ 0.15 = 240

Example: A nursing student scored 68 out of 80 on a practice exam. What is her percentage score? Solution: (68 ÷ 80) × 100 = 85%. This is a 'finding what percentage' problem. Always divide the part by the whole, then multiply by 100.

Example: A hospital reports that 12% of its 450 beds are in the ICU. How many ICU beds does it have? Solution: 0.12 × 450 = 54 beds. This is a 'percentage of a number' problem. Convert the percentage to a decimal first, then multiply.

Example: The price of a textbook was reduced from $85 to $68. What is the percentage decrease? Solution: Find the decrease: $85 - $68 = $17. Divide by the original: $17 ÷ $85 = 0.20 = 20% decrease. Percentage change always uses the original value as the denominator — this is a common trap on the TEAS.

Unit Conversion and Measurement Problems

Unit conversion problems test your ability to switch between measurement systems — metric to metric, customary to customary, and occasionally between the two. The TEAS provides common conversion factors, but you need to know how to use them.

Example: A patient needs 1.5 liters of saline solution. How many milliliters is this? Solution: 1 liter = 1,000 milliliters. So 1.5 × 1,000 = 1,500 mL. For metric conversions, remember the staircase: kilo- (1,000), base unit, centi- (0.01), milli- (0.001). Moving down multiplies, moving up divides.

Example: A baby weighs 7 pounds 8 ounces at birth. What is the baby's weight in ounces? Solution: 1 pound = 16 ounces. So 7 × 16 = 112 ounces + 8 ounces = 120 ounces. Always convert the larger unit first, then add the remainder.

Example: A medication dosage is 5 mg per kilogram of body weight. If a patient weighs 176 pounds, what is the required dosage? (1 kg = 2.2 lbs.) Solution: Convert weight: 176 ÷ 2.2 = 80 kg. Calculate dosage: 80 × 5 = 400 mg. This two-step conversion problem is very common on the TEAS — it requires both unit conversion and multiplication.

Algebra Word Problems

Algebra word problems on the TEAS are generally limited to one-variable and two-step equations. You won't see complex systems of equations or quadratics. The challenge is translating the English description into an algebraic expression.

Example: A nurse works 12-hour shifts. She earns $32 per hour for regular time and $48 per hour for overtime (any hours over 8 in a shift). How much does she earn in one shift? Solution: Regular pay: 8 × $32 = $256. Overtime hours: 12 - 8 = 4 hours. Overtime pay: 4 × $48 = $192. Total: $256 + $192 = $448.

Example: A student needs an average of 80% across 5 exams to pass the course. Her first four exam scores are 75, 82, 78, and 88. What minimum score does she need on the fifth exam? Solution: Total points needed: 80 × 5 = 400. Points earned so far: 75 + 82 + 78 + 88 = 323. Minimum fifth score: 400 - 323 = 77.

Example: The length of a rectangular room is 3 feet more than twice its width. If the perimeter is 48 feet, find the dimensions. Solution: Let width = w. Length = 2w + 3. Perimeter = 2(w) + 2(2w + 3) = 48. Simplify: 2w + 4w + 6 = 48 → 6w = 42 → w = 7 feet. Length = 2(7) + 3 = 17 feet.

Data and Statistics Word Problems

Statistics questions on the TEAS focus on mean, median, mode, range, and basic data interpretation from tables and graphs. These are generally the most straightforward word problems if you know the definitions.

Example: A nursing class has the following exam scores: 72, 85, 91, 68, 85, 77, 93, 85, 80. Find the mean, median, and mode. Solution: Mean = sum ÷ count = 736 ÷ 9 = 81.8 (rounded). For the median, arrange in order: 68, 72, 77, 80, 85, 85, 85, 91, 93. The middle value (5th) is 85. The mode is also 85, appearing three times.

Example: A bar graph shows patient admissions per month. January had 120, February had 95, March had 140, and April had 110. What is the range of admissions? Solution: Range = highest - lowest = 140 - 95 = 45 patients. On the TEAS, always double-check that you're reading the graph values accurately before calculating.

Practice Problems to Try on Your Own

Test yourself with these additional problems. Try solving each one before reading the answer below it.

Problem 1: A pharmacy technician needs to prepare a 250 mL solution that is 40% saline. How many milliliters of pure saline are needed? Answer: 0.40 × 250 = 100 mL of pure saline.

Problem 2: A patient's heart rate decreased from 92 bpm to 78 bpm after medication. What is the percentage decrease, rounded to the nearest whole number? Answer: (92 - 78) ÷ 92 × 100 = 14 ÷ 92 × 100 ≈ 15% decrease.

Problem 3: A clinical trial has 3 men for every 5 women. If there are 120 participants total, how many are women? Answer: Total ratio parts = 3 + 5 = 8. Women = (5/8) × 120 = 75 women.

Problem 4: Convert 98.6°F to Celsius using the formula C = (F - 32) × 5/9. Answer: C = (98.6 - 32) × 5/9 = 66.6 × 5/9 = 37°C — normal body temperature.

Problem 5: The mean of six numbers is 24. Five of the numbers are 18, 22, 27, 30, and 19. What is the sixth number? Answer: Total sum needed = 24 × 6 = 144. Sum of five numbers = 18 + 22 + 27 + 30 + 19 = 116. Sixth number = 144 - 116 = 28.

Final Tips for TEAS Math Word Problems

After working through these examples, you should notice that the math itself is never the hard part — it's always the setup. The TEAS tests mathematical reasoning in context, not raw computation ability. Keep these principles in mind as you continue practicing:

• Always write down what you know and what you need to find. Physical organization prevents mental chaos.
• Watch out for extra information included to distract you. Not every number in a problem is needed for the solution.
• Check your units. If the question asks for milliliters and you calculated liters, you need one more step.
• Use estimation to eliminate wrong answers. If a problem is about someone's daily commute and the answer choices include 500 miles, that's not it.
• Practice under timed conditions. You have about 1.5 minutes per math question — that's comfortable if you practice, but tight if you don't.