Class 6 Maths Worksheet: Algebra Word Problems - Practice solving real-world math problems using algebraic expressions and equations.

Let's solve each problem step-by-step from the Class 6 Maths Worksheet on Algebra – Word Problems.

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1. Think of a number, add 2 to it and then multiply the sum by 6, the result is 42. Number = ?

Let the number be $ x $.

According to the problem:
$$
6(x + 2) = 42
$$

Divide both sides by 6:
$$
x + 2 = 7
$$

Subtract 2:
$$
x = 5
$$

✔ Answer: 5

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2. The side of a regular hexagon is s cm. Find its perimeter.

A regular hexagon has 6 equal sides.

Perimeter = $ 6 \times s = 6s $

✔ Answer: $ 6s $ cm

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3. The number of bacteria in a culture is x now. It becomes square of itself after one week. What will be its number after two weeks?

- After 1 week: $ x^2 $
- After 2 weeks: $ (x^2)^2 = x^4 $

✔ Answer: $ x^4 $

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4. If there are x rows of chairs and each row contains $ x^2 $ chairs. Determine the total number of chairs.

Total chairs = Number of rows × Chairs per row
= $ x \times x^2 = x^3 $

✔ Answer: $ x^3 $

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5. The length of a rectangle is y times its breadth x. The area of the rectangle is

Breadth = $ x $
Length = $ y \times x = xy $

Area = Length × Breadth = $ xy \times x = x^2y $

✔ Answer: $ x^2y $

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6. The length and breadth of a room are $ 3x^2y^3 $ and $ 6x^3y^2 $. Find its area.

Area = Length × Breadth
= $ (3x^2y^3) \times (6x^3y^2) $

Multiply coefficients: $ 3 \times 6 = 18 $

Multiply variables:
- $ x^2 \times x^3 = x^{5} $
- $ y^3 \times y^2 = y^{5} $

So, Area = $ 18x^5y^5 $

✔ Answer: $ 18x^5y^5 $

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7. What is the value of $ x + x + x + \ldots $ (y times)?

Adding $ x $, $ y $ times = $ y \times x = xy $

✔ Answer: $ xy $

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8. A chair costs ₹x. The cost of $ x^2y $ chairs is = ₹______

Cost of one chair = ₹$ x $
Cost of $ x^2y $ chairs = $ x \times x^2y = x^3y $

✔ Answer: ₹ $ x^3y $

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9. A man spends ₹x per week. The total money spent by him in $ xy^2 $ weeks is = ₹______

Money spent per week = ₹$ x $
Number of weeks = $ xy^2 $

Total money = $ x \times xy^2 = x^2y^2 $

✔ Answer: ₹ $ x^2y^2 $

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10. There are 47 boys in the class. This is three more than four times the number of girls. How many girls are there in the class?

Let the number of girls = $ g $

According to the problem:
$$
4g + 3 = 47
$$

Subtract 3:
$$
4g = 44
$$

Divide by 4:
$$
g = 11
$$

✔ Answer: 11 girls

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✔ Final Answers:

| Question | Answer |
|--------|--------|
| 1 | 5 |
| 2 | $ 6s $ cm |
| 3 | $ x^4 $ |
| 4 | $ x^3 $ |
| 5 | $ x^2y $ |
| 6 | $ 18x^5y^5 $ |
| 7 | $ xy $ |
| 8 | ₹ $ x^3y $ |
| 9 | ₹ $ x^2y^2 $ |
| 10 | 11 |

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