Word Problems
Translate real-world situations into linear equations.
Learn
Steps for Word Problems
- Read carefully and identify unknowns
- Define a variable for what you need to find
- Write an equation from the problem
- Solve the equation
- Check your answer in the original problem
Practice
Question 1: Maria has $50. After buying 4 identical notebooks, she has $26 left. What is the cost of each notebook?
Answer
Let n = cost of each notebook. 50 - 4n = 26. -4n = -24. n = $6 per notebook.
Question 2: A number plus 7, then multiplied by 3, equals 30. What is the number?
Answer
3(x + 7) = 30. 3x + 21 = 30. 3x = 9. x = 3.
Question 3: Jake is 5 years older than his sister. The sum of their ages is 27. How old is Jake?
Answer
Sister = x, Jake = x + 5. x + (x + 5) = 27. 2x + 5 = 27. 2x = 22. x = 11. Jake is 16.
Question 4: A rectangle's length is 3 more than twice its width. The perimeter is 48. Find the width.
Answer
w = width, l = 2w + 3. 2(w + 2w + 3) = 48. 2(3w + 3) = 48. 6w + 6 = 48. 6w = 42. w = 7.
Question 5: Tom earns $12 per hour plus a $20 bonus. He earned $80 total. How many hours did he work?
Answer
12h + 20 = 80. 12h = 60. h = 5 hours.
Question 6: The sum of two consecutive numbers is 45. Find the numbers.
Answer
x + (x + 1) = 45. 2x + 1 = 45. 2x = 44. x = 22. Numbers are 22 and 23.
Question 7: A taxi charges $3 base fee plus $2.50 per mile. The total cost was $18. How many miles?
Answer
3 + 2.50m = 18. 2.50m = 15. m = 6 miles.
Question 8: Triple a number decreased by 8 equals 19. Find the number.
Answer
3x - 8 = 19. 3x = 27. x = 9.
Question 9: A store sells shirts for $15 and pants for $25. You buy 3 items totaling $55. How many of each?
Answer
Let s = shirts, p = pants. s + p = 3 and 15s + 25p = 55. If s = 2, p = 1: 15(2) + 25(1) = 55. Check!
Question 10: Half of a number plus 12 equals 20. Find the number.
Answer
x/2 + 12 = 20. x/2 = 8. x = 16.