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Class 7 Maths Chapter 7 Finding the Unknown Notes & Solutions | Ganita Prakash

Class 7 Maths Chapter 7 Finding the Unknown notes and book solutions from Ganita Prakash Part 2 with easy explanations, important concepts, examples and complete textbook question answers for revision and exam preparation.

Finding the Unknown

Grade 7 Mathematics

Ganita Prakash Part-II

Fresh Practice Worksheet

Name:
Class: VII
Roll No.:
Date:

Instructions

  • Read every question carefully.
  • Show all important steps while solving equations.
  • Check your answer whenever possible.
  • Use a letter such as x, y, m or n for an unknown quantity.
  • Do not look at the answer sheet until you have completed the worksheet.

Section A – Warm-Up

Complete the following questions to revise unknowns, equations, LHS and RHS.

1. Fill in the blanks.

(a) An unknown quantity can be represented by a __________.

(b) The two sides of an equation are called the __________ and the __________.

(c) The symbol used to show equality is __________.

(d) Addition and subtraction are __________ operations.

(e) Multiplication and division are __________ operations.

2. Write whether each statement is True or False.

(a) An equation has an equal sign. __________

(b) We can perform an operation on only one side of an equation. __________

(c) The solution of an equation makes the LHS equal to the RHS. __________

(d) x is always equal to 10. __________

(e) Trial and error can sometimes be used to solve an equation. __________

3. Identify the unknown in each expression.

(a) 5x + 7 = 22

Unknown: __________

(b) 9y – 4 = 14

Unknown: __________

(c) 6m = 48

Unknown: __________

(d) 3n + 2 = 17

Unknown: __________

4. For the equation 3x + 5 = 20, write:

(a) LHS = ____________________

(b) RHS = ____________________

(c) Unknown = ____________________

Section B – Solve the Equations

5. Solve: 2x + 7 = 19.

6. Solve: 5y – 8 = 27.

7. Solve: 7m = 63.

8. Solve: n/6 = 8.

9. Solve: 4p + 3 = 31.

10. Solve: 9q – 11 = 34.

11. Solve: 3a + 8 = 2a + 17.

12. Solve: 7b – 5 = 3b + 15.

13. Solve: 5c + 9 = 2c + 24.

14. Solve: 8d – 7 = 5d + 14.

Section C – Find the Mistake

Read each solution carefully. Identify the mistake and solve the equation correctly.

15. A student solved the equation 4x + 6 = 18 as follows:

4x + 6 = 18
4x = 18 + 6
4x = 24
x = 6

Is the solution correct? If not, find and correct the mistake.

16. A student solved 7y – 4 = 24 as follows:

7y = 24 – 4
7y = 20
y = 20/7

Check whether the solution is correct. If not, solve correctly.

17. A student solved 3z + 5 = z + 15 as follows:

3z – z = 15 + 5
2z = 20
z = 10

Find the mistake and write the correct solution.

Section D – Form the Equation

18. A number increased by 9 is 25. Let the number be x.

Write an equation and find x.

19. Three times a number is 42. Let the number be n.

Write an equation and find n.

20. A number decreased by 12 is 30. Let the number be p.

Write an equation and find p.

21. Five times a number increased by 4 is 39. Let the number be x.

Write an equation and find x.

22. Seven times a number decreased by 5 is 30. Let the number be y.

Write an equation and find y.

Section E – Word Problems

23. The sum of a number and 18 is 47. Find the number.

24. The difference between a number and 15 is 28. Find the number.

25. One number is 6 more than another number. Their sum is 42. Find both numbers.

26. The sum of two numbers is 64. One number is three times the other. Find both numbers.

27. A mother is 24 years older than her daughter. Together their ages are 48 years. Find their ages.

28. A notebook costs ₹15 more than a pen. Together they cost ₹75. Find the cost of the pen and the notebook.

29. A taxi charges ₹100 as a fixed charge and ₹20 per kilometre. The total bill is ₹500. How many kilometres were travelled?

30. There are some bicycles and tricycles in a parking area. Together there are 20 vehicles and 46 wheels. How many bicycles and how many tricycles are there?

Section F – Number Puzzles

31. I am a two-digit number. My units digit is 3 more than my tens digit. The sum of my digits is 11. What number am I?

32. I am a two-digit number. My tens digit is twice my units digit. The sum of my digits is 12. What number am I?

33. The sum of three consecutive numbers is 72. Find the numbers.

34. The sum of two consecutive odd numbers is 48. Find the numbers.

35. One-fourth of a number increased by 6 gives the same number. Find the number.

Section G – Patterns and Equations

36. A matchstick pattern has 2n + 1 sticks at position n. How many sticks are needed at position 15?

37. A pattern has 3n + 2 objects at position n. How many objects are there at position 12?

38. A pattern uses 4n + 1 sticks at position n. Can the pattern have exactly 41 sticks? If yes, find the position number.

39. A pattern uses 5n + 2 sticks. Can an arrangement in this pattern use exactly 52 sticks? Explain your answer.

40. The number of tiles in a pattern is 4n. How many tiles are present at position 20?

Section H – Create Your Own Equation

41. Write three different equations whose solution is x = 5.

42. Write three different equations whose solution is y = -3.

43. Create an equation that has no solution. Explain why it has no solution.

44. Create a real-life situation that can be represented by the equation 100x + 50 = 350.

Section I – Challenge Questions

45. Solve:

2(x + 5) = 26

46. Solve:

3(2y – 1) = 21

47. Solve:

4(x – 3) + 5 = 21

48. Solve:

5(2m + 1) = 35

49. Solve:

2x + 7 = 5x – 8

50. A number is multiplied by 4 and then 7 is added. The result is 35. Find the number.

ANSWER SHEET

Use this section after completing the worksheet.

1. (a) letter/letter-number (b) LHS, RHS (c) = (d) inverse (e) inverse
2. (a) True (b) False (c) True (d) False (e) True
3. (a) x (b) y (c) m (d) n
4. (a) 3x + 5 (b) 20 (c) x
5. x = 6
6. y = 7
7. m = 9
8. n = 48
9. p = 7
10. q = 5
11. a = 9
12. b = 5
13. c = 5
14. d = 7
15. Incorrect. The correct solution is: 4x + 6 = 18, 4x = 12, x = 3.
16. Incorrect. The correct solution is: 7y – 4 = 24, 7y = 28, y = 4.
17. Incorrect. The +5 must be moved as -5: 3z + 5 = z + 15, 2z = 10, z = 5.
18. x + 9 = 25, x = 16.
19. 3n = 42, n = 14.
20. p – 12 = 30, p = 42.
21. 5x + 4 = 39, 5x = 35, x = 7.
22. 7y – 5 = 30, 7y = 35, y = 5.
23. x + 18 = 47, x = 29.
24. x – 15 = 28, x = 43.
25. Let the smaller number be x. x + x + 6 = 42. 2x = 36. x = 18. Other number = 24. Answer: 18 and 24.
26. Let the smaller number be x. x + 3x = 64. 4x = 64. x = 16. Other number = 48. Answer: 16 and 48.
27. Let daughter’s age be x. Mother’s age = x + 24. x + x + 24 = 48. 2x = 24. x = 12. Mother = 36. Answer: Daughter 12 years, Mother 36 years.
28. Let pen cost ₹x. Notebook = ₹(x + 15). x + x + 15 = 75. 2x = 60. x = 30. Pen = ₹30, Notebook = ₹45.
29. 100 + 20x = 500. 20x = 400. x = 20 km.
30. Let bicycles = b. Tricycles = 20 – b. 2b + 3(20 – b) = 46. 2b + 60 – 3b = 46. b = 14. Tricycles = 6. Answer: 14 bicycles and 6 tricycles.
31. Let tens digit be x. Units digit = x + 3. x + x + 3 = 11. 2x = 8. x = 4. Units digit = 7. Answer: 47.
32. Let units digit be x. Tens digit = 2x. 2x + x = 12. 3x = 12. x = 4. Tens digit = 8. Answer: 84.
33. Let the numbers be x, x + 1 and x + 2. 3x + 3 = 72. 3x = 69. x = 23. Answer: 23, 24, 25.
34. Let the smaller odd number be x. Next odd number = x + 2. x + x + 2 = 48. 2x = 46. x = 23. Answer: 23 and 25.
35. x/4 + 6 = x. 6 = 3x/4. 24 = 3x. x = 8.
36. 2n + 1 = 2(15) + 1 = 31 sticks.
37. 3(12) + 2 = 38 objects.
38. 4n + 1 = 41. 4n = 40. n = 10. Yes, position 10.
39. 5n + 2 = 52. 5n = 50. n = 10. Yes, position 10.
40. 4(20) = 80 tiles.
41. Many answers are possible. Examples: x + 2 = 7; 2x = 10; x – 3 = 2.
42. Many answers are possible. Examples: y + 3 = 0; 2y = -6; y – 2 = -5.
43. Example: x + 4 = x + 7. Subtracting x gives 4 = 7, which is impossible. Therefore, it has no solution.
44. Example: A product costs ₹100 per item and the delivery charge is ₹50. The total cost is ₹350. Therefore: 100x + 50 = 350.
45. 2(x + 5) = 26. x + 5 = 13. x = 8.
46. 3(2y – 1) = 21. 2y – 1 = 7. 2y = 8. y = 4.
47. 4(x – 3) + 5 = 21. 4(x – 3) = 16. x – 3 = 4. x = 7.
48. 5(2m + 1) = 35. 2m + 1 = 7. 2m = 6. m = 3.
49. 2x + 7 = 5x – 8. 15 = 3x. x = 5.
50. 4x + 7 = 35. 4x = 28. x = 7.
Finding the Unknown – Grade 7 Mathematics
Fresh Practice Worksheet

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