Let’s go through each problem one by one, solve them carefully, and then give the final answers.
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Problem 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
n.
Step 1: Add 2 → n + 2
Step 2: Multiply by 6 → 6(n + 2)
Step 3: Result is 42 → 6(n + 2) = 42
Now solve:
Divide both sides by 6:
n + 2 = 7
Subtract 2:
n = 5
✔ Check: 5 + 2 = 7; 7 × 6 = 42 → Correct!
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Problem 2:
The side of a regular hexagon is s cm. Find its perimeter.
A regular hexagon has 6 equal sides.
Perimeter = 6 × side = 6s cm
✔ Simple and direct.
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Problem 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: x²
After 2 weeks: (x²)² = x⁴
✔ Because squaring x² means multiplying x² × x² = x^(2+2) = x⁴
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Problem 4:
If there are x rows of chairs and each row contains x² chairs. Determine the total number of chairs.
Total chairs = number of rows × chairs per row = x × x² = x³
✔ Because x¹ × x² = x^(1+2) = x³
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Problem 5:
The length of a rectangle is y times its breadth x. The area of the rectangle is?
Breadth = x
Length = y × x = xy
Area = length × breadth = xy × x = x²y
✔ Area = x * (xy) = x²y
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Problem 6:
The length and breadth of a room are 3x²y³ and 6x³y². Find its area.
Area = length × breadth = (3x²y³) × (6x³y²)
Multiply coefficients: 3 × 6 = 18
Multiply x terms: x² × x³ = x⁵
Multiply y terms: y³ × y² = y⁵
So area = 18x⁵y⁵
✔ Verified with exponent rules.
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Problem 7:
What is the value of x + x + x + ... (y times) = ?
Adding x, y times → that’s multiplication: x × y = xy
✔ Example: x + x + x (3 times) = 3x → so y times = xy
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Problem 8:
A chair costs ₹x. The cost of x²y chairs is = ?
Cost = price per chair × number of chairs = x × x²y = x³y
✔ x¹ × x² = x³ → so x³y
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Problem 9:
A man spends ₹x per week. The total money spent by him in xy² weeks is = ?
Total spent = weekly spend × number of weeks = x × xy² = x²y²
✔ x¹ × x¹ = x² → so x²y²
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Problem 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 number of girls = g
“Three more than four times the number of girls” → 4g + 3
This equals 47 → 4g + 3 = 47
Solve:
Subtract 3: 4g = 44
Divide by 4: g = 11
✔ Check: 4×11 = 44; 44 + 3 = 47 → Correct!
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Final Answers:
1. 5
2. 6s
3. x⁴
4. x³
5. x²y
6. 18x⁵y⁵
7. xy
8. x³y
9. x²y²
10. 11
Parent Tip: Review the logic above to help your child master the concept of basic algebra word problems worksheet.
