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Class 8 Maths Worksheet: Linear Equations

Maths worksheets lesson 60: Linear equations in one variable · Set 34 · 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.The length of a rectangle is 13 cm more than its width. Its perimeter is 118 cm. What is its width (in cm)?
  2. 2.A father is 8 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
  3. 3.The length of a rectangle is 1 cm more than its width. Its perimeter is 70 cm. What is its width (in cm)?
  4. 4.The length of a rectangle is 9 cm more than its width. Its perimeter is 74 cm. What is its width (in cm)?
  5. 5.The length of a rectangle is 1 cm more than its width. Its perimeter is 50 cm. What is its width (in cm)?
  6. 6.Solve: 3y + 6 = y + 24. What is y?
  7. 7.A father is 45 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?
  8. 8.A father is 14 years older than his son. In 5 years, the father will be twice as old as his son. How old is the son now?
  9. 9.Solve: 6y + 5 = y + 40. What is y?
  10. 10.The length of a rectangle is 6 cm more than its width. Its perimeter is 116 cm. What is its width (in cm)?
  11. 11.The sum of two consecutive whole numbers is 57. What is the largest of them?
  12. 12.Solve: n/6 + n/5 = 44. What is n?
  13. 13.Solve: 3(m − 1) = 2m + 12. What is m?
  14. 14.A father is 21 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?
  15. 15.Solve: 3(m − 4) = m + 4. What is m?
  16. 16.A father is 42 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?
  17. 17.Solve: t/6 + t/3 = 21. What is t?
  18. 18.The length of a rectangle is 10 cm more than its width. Its perimeter is 84 cm. What is its width (in cm)?
  19. 19.A father is 6 years older than his son. In 1 year, the father will be three times as old as his son. How old is the son now?
  20. 20.The length of a rectangle is 10 cm more than its width. Its perimeter is 60 cm. What is its width (in cm)?
  21. 21.Solve: 7y + 7 = 2y + 27. What is y?
  22. 22.The sum of four consecutive whole numbers is 222. What is the smallest of them?
  23. 23.The length of a rectangle is 1 cm more than its width. Its perimeter is 18 cm. What is its width (in cm)?
  24. 24.Solve: 3(t − 3) = t + 7. What is t?
  25. 25.A father is 20 years older than his son. In 4 years, the father will be three times as old as his son. How old is the son now?
  26. 26.Solve: p/6 + p/2 = 24. What is p?
  27. 27.A father is 18 years older than his son. In 1 year, the father will be three times as old as his son. How old is the son now?
  28. 28.The sum of four consecutive whole numbers is 138. What is the smallest of them?
  29. 29.Solve: 6(y − 3) = 3y + 39. What is y?
  30. 30.A father is 16 years older than his son. In 4 years, the father will be three times as old as his son. How old is the son now?
  31. 31.Solve: t/4 + t/3 = 28. What is t?
  32. 32.A father is 18 years older than his son. In 1 year, the father will be four times as old as his son. How old is the son now?
  33. 33.The length of a rectangle is 2 cm more than its width. Its perimeter is 12 cm. What is its width (in cm)?
  34. 34.Solve: 3(x − 5) = x + 19. What is x?
  35. 35.Solve: t/4 + t/2 = 12. What is t?
  36. 36.Solve: n/2 + n/5 = 14. What is n?
  37. 37.The length of a rectangle is 6 cm more than its width. Its perimeter is 76 cm. What is its width (in cm)?
  38. 38.A father is 57 years older than his son. In 7 years, the father will be four times as old as his son. How old is the son now?
  39. 39.Solve: m/6 + m/5 = 88. What is m?
  40. 40.Solve: 6(n − 5) = 4n + 26. What is n?

Answer key

  1. 23
  2. 3
  3. 17
  4. 14
  5. 12
  6. 9
  7. 12
  8. 9
  9. 7
  10. 26
  11. 29
  12. 120
  13. 15
  14. 2
  15. 8
  16. 9
  17. 42
  18. 16
  19. 2
  20. 10
  21. 4
  22. 54
  23. 4
  24. 8
  25. 6
  26. 36
  27. 8
  28. 33
  29. 19
  30. 4
  31. 48
  32. 5
  33. 2
  34. 17
  35. 16
  36. 20
  37. 16
  38. 12
  39. 240
  40. 28

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