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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 114 · 40 sums
TalentJR

The method (Letters one side, numbers the other): Open brackets: a(x − b) = ax − ab. Fractions: multiply both sides by the LCM of the denominators — x/3 + x/4 = 14 → 4x + 3x = 168. Move letter terms to one side and numbers to the other (change the sign when a term crosses =), then divide. Word problems: consecutive numbers are n, n + 1, n + 2 …; ages in y years are age + y.

NameDateTime takenScore ___ / 40
  1. 1.A father is 33 years older than his son. In 5 years, the father will be four times as old as his son. How old is the son now?
  2. 2.The sum of three consecutive whole numbers is 36. What is the largest of them?
  3. 3.A father is 24 years older than his son. In 3 years, the father will be four times as old as his son. How old is the son now?
  4. 4.Solve: y/2 + y/5 = 56. What is y?
  5. 5.The length of a rectangle is 12 cm more than its width. Its perimeter is 56 cm. What is its width (in cm)?
  6. 6.The length of a rectangle is 10 cm more than its width. Its perimeter is 112 cm. What is its width (in cm)?
  7. 7.Solve: y/2 + y/4 = 6. What is y?
  8. 8.The sum of two consecutive whole numbers is 39. What is the largest of them?
  9. 9.Solve: 8t + 11 = 7t + 18. What is t?
  10. 10.Solve: y/2 + y/4 = 21. What is y?
  11. 11.Solve: 3(x − 3) = 2x + 10. What is x?
  12. 12.The sum of four consecutive whole numbers is 102. What is the smallest of them?
  13. 13.Solve: 4(y − 2) = 2y + 12. What is y?
  14. 14.The sum of three consecutive whole numbers is 45. What is the largest of them?
  15. 15.Solve: 4(p − 2) = p + 25. What is p?
  16. 16.Solve: n/3 + n/4 = 42. What is n?
  17. 17.The length of a rectangle is 7 cm more than its width. Its perimeter is 22 cm. What is its width (in cm)?
  18. 18.Solve: 4p + 13 = 2p + 29. What is p?
  19. 19.Solve: m/6 + m/2 = 8. What is m?
  20. 20.A father is 28 years older than his son. In 7 years, the father will be three times as old as his son. How old is the son now?
  21. 21.A father is 54 years older than his son. In 6 years, the father will be four times as old as his son. How old is the son now?
  22. 22.Solve: 3(y − 4) = y + 6. What is y?
  23. 23.Solve: 5(x − 4) = x + 40. What is x?
  24. 24.A father is 34 years older than his son. In 5 years, the father will be three times as old as his son. How old is the son now?
  25. 25.A father is 9 years older than his son. In 4 years, the father will be twice as old as his son. How old is the son now?
  26. 26.The sum of four consecutive whole numbers is 26. What is the largest of them?
  27. 27.Solve: 6(x − 2) = x + 13. What is x?
  28. 28.Solve: 6p + 4 = p + 24. What is p?
  29. 29.The length of a rectangle is 10 cm more than its width. Its perimeter is 28 cm. What is its width (in cm)?
  30. 30.A father is 39 years older than his son. In 3 years, the father will be four times as old as his son. How old is the son now?
  31. 31.Solve: t/3 + t/6 = 18. What is t?
  32. 32.The length of a rectangle is 5 cm more than its width. Its perimeter is 86 cm. What is its width (in cm)?
  33. 33.Solve: n/6 + n/2 = 20. What is n?
  34. 34.A father is 11 years older than his son. In 3 years, the father will be twice as old as his son. How old is the son now?
  35. 35.The sum of three consecutive whole numbers is 39. What is the smallest of them?
  36. 36.The sum of two consecutive whole numbers is 91. What is the largest of them?
  37. 37.Solve: 4(y − 1) = 3y + 9. What is y?
  38. 38.A father is 10 years older than his son. In 7 years, the father will be twice as old as his son. How old is the son now?
  39. 39.The length of a rectangle is 11 cm more than its width. Its perimeter is 46 cm. What is its width (in cm)?
  40. 40.A father is 11 years older than his son. In 2 years, the father will be twice as old as his son. How old is the son now?

Answer key

  1. 6
  2. 13
  3. 5
  4. 80
  5. 8
  6. 23
  7. 8
  8. 20
  9. 7
  10. 28
  11. 19
  12. 24
  13. 10
  14. 16
  15. 11
  16. 72
  17. 2
  18. 8
  19. 12
  20. 7
  21. 12
  22. 9
  23. 15
  24. 12
  25. 5
  26. 8
  27. 5
  28. 4
  29. 2
  30. 10
  31. 36
  32. 19
  33. 30
  34. 8
  35. 12
  36. 46
  37. 13
  38. 3
  39. 6
  40. 9

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