Word Problems
Learning Objectives
In this lesson, you will learn to:
- Translate word problems into linear equations
- Identify key words that indicate mathematical operations
- Set up and solve real-world application problems
- Verify solutions in context of the original problem
Practice Quiz
Solve these 10 word problems. Click each question to reveal the answer and explanation.
Question 1: A number increased by 7 equals 23. What is the number?
Answer: 16
Solution: Let x = the number. Equation: x + 7 = 23. Solve: x = 16.
Question 2: The sum of three consecutive integers is 42. Find the integers.
Answer: 13, 14, 15
Solution: Let x = first integer. Equation: x + (x+1) + (x+2) = 42. Simplify: 3x + 3 = 42. Solve: x = 13.
Question 3: Sarah has twice as many books as Tom. Together they have 36 books. How many does Sarah have?
Answer: 24 books
Solution: Let x = Tom's books. Sarah has 2x. Equation: x + 2x = 36. Solve: 3x = 36, x = 12. Sarah: 2(12) = 24.
Question 4: A rectangle's length is 5 more than its width. The perimeter is 42 cm. Find the dimensions.
Answer: Width = 8 cm, Length = 13 cm
Solution: Let w = width, l = w + 5. Perimeter: 2w + 2(w+5) = 42. Solve: 4w + 10 = 42, w = 8. Length = 13.
Question 5: A phone plan costs $25 per month plus $0.10 per text. If the bill is $35, how many texts were sent?
Answer: 100 texts
Solution: Let x = texts. Equation: 25 + 0.10x = 35. Solve: 0.10x = 10, x = 100.
Question 6: Five less than twice a number is 17. Find the number.
Answer: 11
Solution: Let x = the number. Equation: 2x - 5 = 17. Add 5: 2x = 22. Divide: x = 11.
Question 7: A car travels at 60 mph. How long will it take to travel 210 miles?
Answer: 3.5 hours
Solution: Distance = Rate x Time. 210 = 60t. Solve: t = 210/60 = 3.5 hours.
Question 8: The sum of two numbers is 50. One number is 8 more than the other. Find both numbers.
Answer: 21 and 29
Solution: Let x = smaller number. Equation: x + (x + 8) = 50. Solve: 2x = 42, x = 21. Other number: 29.
Question 9: A store sells pens for $2 and notebooks for $5. If you buy 7 items for $23, how many pens did you buy?
Answer: 4 pens
Solution: Let p = pens, n = notebooks. System: p + n = 7 and 2p + 5n = 23. From first: n = 7-p. Substitute: 2p + 5(7-p) = 23. Solve: -3p = -12, p = 4.
Question 10: After a 20% discount, a jacket costs $48. What was the original price?
Answer: $60
Solution: Let x = original price. After 20% off, you pay 80%. Equation: 0.80x = 48. Solve: x = 60.
Next Steps
- Practice identifying key words in word problems
- Try writing your own word problems
- Move on to common mistakes to avoid errors