How to solve multi-step word problems
TEAS 7 outline: Solve one- or multi-step real-world problems with real numbers
- Plan, solve, check: read twice and mark what the question asks.
- Write a unit next to every in-between answer.
- "Less than" flips the order: six less than 4n is 4n − 6.
- Fixed fee plus rate: subtract the fee first, then divide by the rate.
- Let the story decide how to round a remainder.
Key facts
- Read the problem twice and mark what the question asks for before doing any math.
- Key words: sum, total, more than → add; difference, less than → subtract; product, times, of → multiply; quotient, divided by, split equally → divide; is → equals.
- "Less than" reverses the order: six less than 4n is 4n − 6.
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- Label every in-between answer with its unit (dollars, tablets, hours) so you know what it stands for.
- A fixed fee plus a rate fits fixed amount + rate × number = total; subtract the fixed amount before dividing by the rate.
- When division leaves a remainder, the story decides whether you round down, round up or keep the decimal.
- Check that the answer is reasonable and answers the exact question (for example, money left, not money spent).
Quick check1 question · 2 more at the end
A pharmacy technician filled 30 prescriptions this morning. That is six less than four times the number she filled yesterday afternoon. If n is the number she filled yesterday afternoon, which equation represents this situation?
Correct answer: B.
"Four times the number" is 4n, and "six less than" 4n means start with 4n and subtract 6, so 4n − 6. The word "is" becomes the equal sign: 4n − 6 = 30, which gives n = 9. Remember that "less than" reverses the order of the words.
A This writes the subtraction in the order the words appear; "six less than 4n" means 4n − 6, not 6 − 4n.
B Correct: four times n, minus 6, equals 30.
C This subtracts 6 from n before multiplying, which would be "four times six less than the number."
D This treats "less than" as addition; "less than" means subtract.
Full lesson
Each part starts with its main idea. Open a part when you want the details.
The short answer: Solve a multi-step word problem in three moves. Plan: read it twice, name exactly what the question asks for, and list the facts you need. Solve: translate the words into operations or an equation and work one labeled step at a time. Check: make sure the answer is reasonable and answers the exact question asked.
1 What is the plan-solve-check method?Every word problem gets easier when you plan, solve, then check. 1 min
Every word problem gets easier when you plan, solve, then check. If a long problem makes your mind go blank, slow down and do only the first move.
- Plan. Read it twice. Underline the exact question, then list the numbers you need.
- Solve. Translate words into math and do one step at a time, writing a unit next to each result.
- Check. Ask "Is this reasonable?" and "Did I answer what was asked?"
Key words point to the operation:
| Words in the problem | Operation |
|---|---|
| sum, total, more than, increased by | add (+) |
| difference, less than, decreased by | subtract (−) |
| product, times, of, twice | multiply (×) |
| quotient, divided by, ratio of, split equally | divide (÷) |
| is, equals, makes | = |
The one rule: "less than" flips the order. "Six less than 4n" means start with 4n and take away 6, so 4n − 6.
2 How do you handle a shopping or budget problem?Find the total cost first, then compare it with the money available. 1 min
Find the total cost first, then compare it with the money available. Example: Keisha buys 3 sets of scrubs at $24.50 each and shoes for $62 with a $150 gift card. How much is left on the card?
- Plan: the question asks for money left, not money spent.
- Scrubs: 3 × $24.50 = $73.50.
- Total spent: $73.50 + $62 = $135.50.
- Money left: $150 − $135.50 = $14.50.
- Check: $14.50 is small and positive, and $135.50 + $14.50 = $150.
Classic wrong turn: stopping at $135.50. That number is real, but it answers a different question.
3 What if there is a fixed fee plus a rate?Take away the fixed fee first, then divide by the rate. 1 min
Take away the fixed fee first, then divide by the rate. Example: a wheelchair rental costs a $40 delivery fee plus $15 per day, and the bill is $145. How many days was it rented?
- Name the unknown: let d = number of days.
- Translate: 40 + 15d = 145.
- Subtract 40 from both sides: 15d = 105.
- Divide both sides by 15: d = 7 days.
- Check: $40 + 7 × $15 = $40 + $105 = $145.
Classic wrong turn: dividing 145 ÷ 15 ≈ 9.7 days. That ignores the delivery fee, and a rental day count should come out whole.
4 What do you do with a leftover remainder?Let the story decide whether to round down, round up or keep the decimal. 1 min
Let the story decide whether to round down, round up or keep the decimal. Example: a bottle holds 45 tablets, and the label says 2 tablets three times a day. How many full days will the bottle last?
- Tablets per day: 2 × 3 = 6 tablets.
- Days: 45 ÷ 6 = 7.5.
- The question asks for full days, so round down: 7 full days, with 3 tablets left over.
- Check: 7 × 6 = 42 tablets, and 45 − 42 = 3.
Classic wrong turn: dividing 45 ÷ 2 = 22.5 days. That uses only one of the two rates in the problem.
5 When should you use the calculator?Use mental math for easy steps and the calculator for decimals and money. 1 min
Use mental math for easy steps and the calculator for decimals and money. The TEAS has a basic on-screen calculator, but it will not set up the problem for you.
- Mental math: 2 × 3, 45 ÷ 6, 145 − 40.
- Calculator: 3 × 24.50 or 162 ÷ 14.50.
- Estimate first: scrubs cost about $25 each, so 3 sets is about $75. If the calculator says $735, you hit a wrong key.
Common mistakes
The traps students fall into most. Read these before you practice.
Watch out: Answer the question asked, not the first number you calculate: the total spent is not the money left over.
Watch out: "Seven less than x" is x − 7, not 7 − x.
Watch out: Take the fixed fee out first: (145 − 40) ÷ 15, not 145 ÷ 15.
Watch out: Use every rate in the problem: 2 tablets three times a day is 6 tablets a day, not 2.
Watch out: Round by the story, not by habit: if 162 ÷ 14.50 ≈ 11.2 items, you can afford 11, not 12.
How to remember it
Read twice, write units, and reread the question before you answer. A handy hook is "What, Work, Wise?": What is it asking? Work it one step at a time. Is the answer wise (reasonable)?
Self-check:
- Translate "seven less than three times a number is 20" into an equation.
- Solve it and label your answer.
- Put your answer back into the sentence to see if it is true.
Show answers
- 3n − 7 = 20.
- Let n = the number.
- "Three times a number" is 3n. "Seven less than" that flips the order: 3n − 7.
- "Is 20" means = 20.
- n = 9 (the number is 9).
- Add 7 to both sides: 3n = 27.
- Divide both sides by 3: n = 9.
- It is true.
- Three times 9 is 27.
- Seven less than 27 is 27 − 7 = 20.