Class 7 Chapter 7 Maths Worksheet: Finding the Unknown

Here is another chapter, from Ganita Prakash, textbook of mathematics for Grade 7, Part II. Presenting the worksheet, which focuses on forming equations and solving them step-by-step using balance logic, patterns, and inverse operations. An answer key with hints is included after the questions.

Class 7 Mathematics – Finding the Unknown (Equations)

A. Balance Logic: Unknown Weights

1. A balance scale is perfectly balanced.
   Left pan: 2 sacks + 6 kg
   Right pan: 18 kg
   Find the weight of 1 sack.
2. A balance scale is perfectly balanced.
   Left pan: 3 identical boxes + 4 kg
   Right pan: 25 kg
   Find the weight of 1 box.
3. A balance scale is perfectly balanced.
   Left pan: 2 balls + 7 kg
   Right pan: 1 ball + 19 kg
   Find the weight of 1 ball.
4. A balance scale is perfectly balanced.
   Left pan: 5 identical packets
   Right pan: 2 packets + 27 kg
   Find the weight of 1 packet.
5. A balance scale is perfectly balanced.
   Left pan: 4 identical cans + 12 kg
   Right pan: 36 kg
   Find the weight of 1 can.

B. Matchstick & Pattern Equations

1. A matchstick pattern uses 2n + 1 sticks at position n.
   Find the position number when the pattern uses 99 sticks.
2. In another pattern, the number of sticks at step n is 3n + 2.
   Find n when the pattern uses 125 sticks.
3. The number of tiles in a design at step k is 3k + 1.
   Can the design use exactly 100 tiles at some step? If yes, find k.
4. A pattern uses 2n + 1 sticks at position n.
   Is it possible to have exactly 200 sticks in this pattern?
   Write a clear reason.

C. Use the “Do the Same on Both Sides” Rule

1. It is known that: 14593 – 1459 + 145 – 14 + 88 = 13353.
   Find the value of: 14593 – 1459 + 145 – 14.
2. It is known that: 23 × 41 × 11 × 8 × 7 = 5,80,888.
   Find the value of: 23 × 41 × 11 × 8.
3. It is known that: P + 36 = 250.
   Find P.
4. It is known that: Q ÷ 9 = 14.
   Find Q.

D. Solve These Equations (No Guessing Games)

1. 2y = 60
2. 5x – 3 = –8
3. 13 – z = 8
4. k + 8 = 12 – k
5. 7m = m – 3
6. 3n = 10 + n

E. Word Problems: Turn the Story into an Equation

1. The weight of a brick is 1 kg more than half its weight.
   Find the weight of the brick.
2. One quarter of a number increased by 9 gives the same number.
   Find the number.
3. A student buys identical pens. The total cost of 6 pens is ₹90.
   Find the cost of 1 pen.
4. In a cricket practice, a coach says: “Your total runs are 12 more than twice your sixes.”
   If the total runs are 46, find the number of sixes.

F. Mind the Mistake, Mend the Mistake

1. Solve and check the steps:
   4x + 6 = 10
   Student’s steps:
   4x = 10 + 6
   4x = 16
   x = 4
   Find the mistake (if any), correct it, and give the right value of x.
2. Solve and check the steps:
   2v – 4 = 6
   Student’s steps:
   v – 4 = 6 – 2
   v – 4 = 4
   v = 8
   Find the mistake (if any), correct it, and give the right value of v.
3. Solve and check the steps:
   5z + 2 = 3z – 4
   Student’s steps:
   5z + 3z = –4 + 2
   8z = –2
   z = –2
   Find the mistake (if any), correct it, and give the right value of z.
4. Solve and check the steps:
   3x + 1 = –12
   Student’s steps:
   x + 1 = –12
   x + 1 = –4
   x = –5
   Find the mistake (if any), correct it, and give the right value of x.

Answer Key with Hints (Step-by-step)

A. Balance Logic: Unknown Weights

1. Answer: 6 kg
   Hint: Write equation: 2s + 6 = 18. Subtract 6 from both sides, then divide by 2.
2. Answer: 7 kg
   Hint: 3b + 4 = 25 → 3b = 21 → b = 7.
3. Answer: 12 kg
   Hint: 2t + 7 = t + 19. Subtract t from both sides, then subtract 7.
4. Answer: 9 kg
   Hint: 5p = 2p + 27 → 3p = 27 → p = 9.
5. Answer: 6 kg
   Hint: 4c + 12 = 36 → 4c = 24 → c = 6.

B. Matchstick & Pattern Equations

1. Answer: n = 49
   Hint: 2n + 1 = 99 → 2n = 98 → n = 49.
2. Answer: n = 41
   Hint: 3n + 2 = 125 → 3n = 123 → n = 41.
3. Answer: Yes, k = 33
   Hint: 3k + 1 = 100 → 3k = 99 → k = 33.
4. Answer: Not possible
   Hint: If 2n + 1 = 200, then 2n = 199, but 199 is odd, so n is not a whole number. Patterns need whole-number steps.

C. Use the “Do the Same on Both Sides” Rule

1. Answer: 13265
   Hint: The expression plus 88 equals 13353. So remove 88 from both sides: 13353 – 88 = 13265.
2. Answer: 82,984
   Hint: Divide both sides by 7: 5,80,888 ÷ 7 = 82,984.
3. Answer: 214
   Hint: P + 36 = 250 → P = 250 – 36 = 214.
4. Answer: 126
   Hint: Q ÷ 9 = 14 → Q = 14 × 9 = 126.

D. Solve These Equations (No Guessing Games)

1. Answer: y = 30
   Hint: Divide both sides by 2.
2. Answer: x = –1
   Hint: 5x – 3 = –8 → 5x = –5 → x = –1.
3. Answer: z = 5
   Hint: 13 – z = 8 → –z = 8 – 13 = –5 → z = 5.
4. Answer: k = 2
   Hint: k + 8 = 12 – k → 2k = 4 → k = 2.
5. Answer: m = –1/2
   Hint: 7m = m – 3 → 6m = –3 → m = –3/6 = –1/2.
6. Answer: n = 5
   Hint: 3n = 10 + n → 2n = 10 → n = 5.

E. Word Problems: Turn the Story into an Equation

1. Answer: 2 kg
   Hint: Let weight = w. Statement: w = (w/2) + 1. Subtract w/2 from both sides: w/2 = 1 → w = 2.
2. Answer: 12
   Hint: Let number = N. N/4 + 9 = N → 9 = N – N/4 = 3N/4 → N = 12.
3. Answer: ₹15
   Hint: 6p = 90 → p = 90 ÷ 6 = 15.
4. Answer: 17 sixes
   Hint: Let sixes = s. Total runs: 2s + 12 = 46 → 2s = 34 → s = 17.

F. Mind the Mistake, Mend the Mistake

1. Answer: x = 1
   Hint: Mistake is sign change. 4x + 6 = 10 → 4x = 10 – 6 = 4 → x = 1.
2. Answer: v = 5
   Hint: Mistake is dividing only one term. Correct: 2v – 4 = 6 → 2v = 10 → v = 5.
3. Answer: z = –3
   Hint: The move is wrong: +2 should go to the other side as –2.
   5z + 2 = 3z – 4 → 5z – 3z = –4 – 2 → 2z = –6 → z = –3.
4. Answer: x = –13/3
   Hint: Mistake is dividing the whole LHS incorrectly.
   3x + 1 = –12 → 3x = –13 → x = –13/3.

Other Class 7 Maths worksheet

• Class 7 Maths Chapter 1 Worksheet: Large Numbers Around Us
• Class 7 Maths Chapter 2 Worksheet: Arithmetic Expressions
• Class 7 Maths Chapter 3 Worksheet: A Peek Beyond the Point
• Class 7 Maths Chapter 4 Worksheet: Another Peek Beyond the Point
• Class 7 Maths Chapter 6 Worksheet: Number Play
• Class 7 Maths Chapter 8 Worksheet: Working with Fractions