Finding the Unknown Class 7 Maths Worksheet with Answers Chapter 7

Ganita Prakash Part-II, Grade 7, Textbook of Mathematics – Chapter 7 is called “Finding the Unknown”. This is your first step into algebra. Sometimes a number is hidden from us. Our job is to find it. We give that hidden number a letter name – like x, y or n. And then we try to its value.

The chapter opens up with a weighing scale. A scale stays balanced only when both pans carry equal weight. From this one picture comes the biggest rule of the chapter: whatever you do to one side of an equation, do exactly the same to the other side. Add, subtract, multiply or divide, you can do all this untill you do on the both sides in the same way. This is the trick behind solving every equation.

Next you learn what an equation is. An equation is two expressions joined by an “=” sign. The part on the left is the LHS (Left Hand Side). The part on the right is the RHS (Right Hand Side). To “solve” the equation means to find the value of the letter that makes LHS = RHS. Once your two sides match, you have your answer.

This worksheet covers all the key skills from the chapter. The main ones are:

• Finding unknown weights on a balance scale
• Framing an equation from a pattern or a story
• Understanding LHS, RHS and what a solution means
• Solving by trial and error
• Solving step by step using the balancing method
• Using inverse operations (add ↔ subtract, multiply ↔ divide)
• Equations with the unknown on both sides
• Word problems – money, savings, marbles, age and number-machine puzzles
• Writing your own equation for a given solution

Very important points and formulas to remember:

• The balancing rule: If you do the same operation to both sides, the equation stays true. This is your main tool.
• Move a term across the “=” sign: When a term crosses over, its sign flips. So 2y + 7 = 21 becomes 2y = 21 − 7.
• Matchstick pattern: Number of sticks at position n = 2n + 1. Use this to find any step in the sequence.
• Brahmagupta’s shortcut: For any equation of the form Ax + B = Cx + D, the answer is x = (D − B) ÷ (A − C). A gift from ancient Indian maths!
• Always check your answer: Put your value back into the equation. If LHS = RHS, you are correct.

Write each step neatly, one below the other. In solving algebra you require more of patience, and not speed.

To help you build up slowly, the questions in this worksheet move through four levels – Basic, Standard, Advanced and HOTS. A full answer key is placed right after the last question so you can check your work yourself.

Class 7 Maths Worksheet – Chapter 7: Finding the Unknown

Basic

1. Solve the equations:
   • x + 7 = 15
   • y − 9 = 12
   • 4z = 28
   • p ÷ 3 = 8
2. Find the unknown:
   • 3a + 5 = 20
   • 6b − 4 = 14
   • 5c + 12 = 47
   • 8d − 9 = 31
3. Fill in the blanks:
   • 2n + 1 = 19, so n = ______
   • 5m − 3 = 22, so m = ______
   • 7p = 56, so p = ______
   • q/4 = 6, so q = ______
4. Check whether the given value is a solution:
   • x = 4 for 3x + 2 = 14
   • y = 6 for 5y − 8 = 20
   • z = 3 for 4z + 7 = 20
5. A number increased by 18 is 45. Form an equation and find the number.
6. Five identical notebooks cost ₹150. Form an equation and find the cost of one notebook.
7. The expression 2n + 1 gives the number of matchsticks in the nth arrangement.
   Find the number of matchsticks in positions:
   • 5
   • 12
   • 30
8. Find the position number of a matchstick arrangement that uses:
   • 31 sticks
   • 99 sticks
   • 200 sticks

   Use 2n + 1 for the number of sticks.

Standard

1. Solve:
   • 7x + 4 = 39
   • 9y − 5 = 58
   • 6a + 11 = 47
   • 4b − 13 = 31
2. Solve the equations involving brackets:
   • 5(x + 2) = 35
   • 3(y − 4) = 18
   • 2(7 − n) = 8
   • 4(p + 3) = 28
3. A taxi driver charges a fixed fee of ₹800 per day plus ₹20 per kilometre travelled.
   If the total fare is ₹2200, how many kilometres were travelled?
4. The sum of two numbers is 76. One number is three times the other.
   Find both numbers.
5. A fruit juice costs ₹15 less than a chocolate milkshake. If 4 fruit juices and 7 milkshakes cost ₹600,
   find the price of each.
6. The height of a giraffe is 2 1/2 metres more than half its height.
   Find the height of the giraffe.
7. Given 28p − 36 = 98, find:
   • 14p − 19
   • 28p − 38
8. Write an equation and solve:
   • A number decreased by 14 equals 29.
   • Seven times a number is 91.
   • Four more than twice a number is 30.

Advance

1. Solve:
   • 3x + 8 = 2x + 19
   • 5y − 7 = 3y + 13
   • 8p + 12 = 5p + 42
   • 6m − 9 = 2m + 19
2. Solve:
   • −3(u + 2) = 2(u − 1)
   • 3 − 7s = 7 − 3s
   • 2x + 1 = 6 − (2x − 3)
3. The perimeter of a rectangle is 54 cm. Its length is 5 cm more than its width.
   Find its length and width.
4. A mother is 24 years older than her daughter. Their ages add up to 52 years.
   Find their present ages.
5. In a class, the number of girls is 8 more than the number of boys. If there are 44 students in total,
   find the number of boys and girls.
6. A shopkeeper has some ₹10 and ₹20 notes. The total number of notes is 35 and their total value is ₹500.
   Find the number of notes of each type.
7. There are children and donkeys on a beach. Together, they have 28 heads and 80 feet.
   Find the number of children and donkeys.
8. A three-digit number has digits whose sum is 15. The hundreds digit is twice the tens digit,
   and the ones digit is 3 more than the tens digit. Find the number.

HOTS

1. A number is increased by 36 and becomes ten times itself. Find the number.
2. The first person receives an amount x. The second receives twice as much as the first,
   the third receives three times as much as the second, and the fourth receives four times as much as the third.
   If the total distributed amount is ₹132, find the amount received by the first person.
3. Explain why the following number trick always gives 8:
   • Think of a number.
   • Multiply it by 2.
   • Add 10.
   • Divide by 2.
   • Subtract the original number.
   • Add 3.
4. The angles of a triangle are x, x + 10 and x + 20 degrees.
   Find all three angles.
5. A father is four times as old as his son. After 10 years, the father will be twice as old as his son.
   Find their present ages.
6. A two-digit number has a tens digit that is 3 more than its units digit. The sum of its digits is 11.
   Find the number.
7. A box contains red and blue balls. There are 24 balls in total. The number of red balls is twice the number of blue balls.
   How many red and blue balls are there?
8. Find a number such that when it is divided by 5 and then increased by 7, the result is 19.
   Form and solve an equation.

Answer Key

Basic – Answers

1. • x + 7 = 15, so x = 15 − 7 = 8.
   • y − 9 = 12, so y = 12 + 9 = 21.
   • 4z = 28, so z = 28 ÷ 4 = 7.
   • p ÷ 3 = 8, so p = 8 × 3 = 24.
2. • 3a + 5 = 20 gives 3a = 15, so a = 5.
   • 6b − 4 = 14 gives 6b = 18, so b = 3.
   • 5c + 12 = 47 gives 5c = 35, so c = 7.
   • 8d − 9 = 31 gives 8d = 40, so d = 5.
3. • 2n + 1 = 19 gives n = 9.
   • 5m − 3 = 22 gives m = 5.
   • 7p = 56 gives p = 8.
   • q/4 = 6 gives q = 24.
4. • For x = 4, 3x + 2 = 3 × 4 + 2 = 14. So, x = 4 is a solution.
   • For y = 6, 5y − 8 = 30 − 8 = 22, not 20. So, y = 6 is not a solution.
   • For z = 3, 4z + 7 = 12 + 7 = 19, not 20. So, z = 3 is not a solution.
5. Let the number be x. Then x + 18 = 45.
   x = 45 − 18 = 27.
6. Let the cost of one notebook be ₹x.
   5x = 150, so x = 150 ÷ 5 = ₹30.
7. • For n = 5, 2n + 1 = 11 sticks.
   • For n = 12, 2n + 1 = 25 sticks.
   • For n = 30, 2n + 1 = 61 sticks.
8. • 2n + 1 = 31 gives n = 15.
   • 2n + 1 = 99 gives n = 49.
   • 2n + 1 = 200 gives n = 99.5. So, no position is possible.

Standard – Answers

1. • 7x + 4 = 39 gives x = 5.
   • 9y − 5 = 58 gives y = 7.
   • 6a + 11 = 47 gives a = 6.
   • 4b − 13 = 31 gives b = 11.
2. • 5(x + 2) = 35 gives x + 2 = 7, so x = 5.
   • 3(y − 4) = 18 gives y − 4 = 6, so y = 10.
   • 2(7 − n) = 8 gives 7 − n = 4, so n = 3.
   • 4(p + 3) = 28 gives p + 3 = 7, so p = 4.
3. Let the kilometres travelled be x.
   800 + 20x = 2200
   20x = 1400, so x = 70 km.
4. Let the smaller number be x. The other number is 3x.
   x + 3x = 76
   4x = 76, so x = 19.
   The numbers are 19 and 57.
5. Let the cost of one milkshake be ₹x. Then one fruit juice costs ₹(x − 15).
   4(x − 15) + 7x = 600
   11x = 660, so x = 60.
   Milkshake = ₹60, fruit juice = ₹45.
6. Let the giraffe’s height be x metres.
   x = x/2 + 2 1/2
   x/2 = 2 1/2, so x = 5 m.
7. From 28p − 36 = 98, we get 28p = 134 and 14p = 67.
   • 14p − 19 = 67 − 19 = 48.
   • 28p − 38 = 134 − 38 = 96.
8. • x − 14 = 29 gives x = 43.
   • 7x = 91 gives x = 13.
   • 2x + 4 = 30 gives x = 13.

Advance – Answers

1. • 3x + 8 = 2x + 19 gives x = 11.
   • 5y − 7 = 3y + 13 gives 2y = 20, so y = 10.
   • 8p + 12 = 5p + 42 gives 3p = 30, so p = 10.
   • 6m − 9 = 2m + 19 gives 4m = 28, so m = 7.
2. • −3(u + 2) = 2(u − 1) gives u = −4/5.
   • 3 − 7s = 7 − 3s gives −4s = 4, so s = −1.
   • 2x + 1 = 6 − (2x − 3) gives 4x = 8, so x = 2.
3. Let the width be x cm. Then length = x + 5 cm.
   2(x + x + 5) = 54
   4x + 10 = 54, so x = 11.
   Width = 11 cm; length = 16 cm.
4. Let the daughter’s age be x years. Mother’s age is x + 24 years.
   x + x + 24 = 52
   2x = 28, so x = 14.
   Daughter = 14 years; mother = 38 years.
5. Let the number of boys be x. Girls = x + 8.
   x + x + 8 = 44
   2x = 36, so x = 18.
   Boys = 18; girls = 26.
6. Let the number of ₹10 notes be x. Then ₹20 notes = 35 − x.
   10x + 20(35 − x) = 500
   −10x = −200, so x = 20.
   ₹10 notes = 20; ₹20 notes = 15.
7. Let the number of donkeys be x. Children = 28 − x.
   4x + 2(28 − x) = 80
   2x = 24, so x = 12.
   Donkeys = 12; children = 16.
8. Let the tens digit be x. Hundreds digit = 2x and ones digit = x + 3.
   2x + x + x + 3 = 15
   4x = 12, so x = 3.
   The number is 639.

HOTS – Answers

1. Let the number be x.
   x + 36 = 10x
   36 = 9x, so x = 4.
2. First person = x
   Second person = 2x
   Third person = 3(2x) = 6x
   Fourth person = 4(6x) = 24x
   x + 2x + 6x + 24x = 132
   33x = 132, so x = ₹4.
3. Let the original number be x.
   
   x → 2x → 2x + 10 → x + 5 → 5 → 8
   
   Therefore, the result is always 8, whatever number is chosen initially.
4. x + (x + 10) + (x + 20) = 180
   3x + 30 = 180, so x = 50.
   The angles are 50°, 60° and 70°.
5. Let the son’s present age be x years. Father’s age is 4x years.
   4x + 10 = 2(x + 10)
   4x + 10 = 2x + 20
   2x = 10, so x = 5.
   Son = 5 years; father = 20 years.
6. Let the units digit be x. Tens digit = x + 3.
   x + (x + 3) = 11
   2x = 8, so x = 4.
   The number is 74.
7. Let the number of blue balls be x. Red balls = 2x.
   x + 2x = 24
   3x = 24, so x = 8.
   Blue balls = 8; red balls = 16.
8. Let the number be x.
   x/5 + 7 = 19
   x/5 = 12
   x = 60.

Other Class 7 Maths worksheet

Ganita Prakash Part-I, Grade 7

• Large Numbers Around Us Class 7 Maths Worksheet
• Arithmetic Expressions Class 7 Maths Worksheet
• A Peek Beyond the Point Class 7 Maths Worksheet
• Number Play Class 7 Maths Worksheet
• Working with Fractions Class 7 Maths Worksheet

Ganita Prakash Part-II, Grade 7

• Operations with Integers Class 7 Maths Worksheet
• Another Peek Beyond the Point Class 7 Maths Worksheet
• Finding the Unknown Class 7 Maths Worksheet

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