Let's solve each problem step by step with clear explanations.
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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:
> (x + 2) × 6 = 42
Divide both sides by 6:
> x + 2 = 7
Subtract 2 from both sides:
> 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 = sum of all sides = 6 × s =
6s cm
✔ 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?
- Now: x
- After 1 week: x²
- After 2 weeks: (x²)² =
x⁴
✔ Answer: x⁴
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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
✔ Answer: x³
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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 × x = xy
Area = length × breadth = xy × x =
x²y
✔ Answer: x²y
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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
Add exponents of like bases:
x² × x³ = x⁵
y³ × y² = y⁵
So, Area =
18x⁵y⁵
✔ Answer: 18x⁵y⁵
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7. What is the value of x + x + x + ... (y times) =
Adding x, y times means: x × y =
xy
✔ Answer: xy
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8. A chair costs ₹x. The cost of x²y chairs is =
Cost of 1 chair = ₹x
Cost of x²y chairs = x × x²y =
x³y
✔ Answer: ₹ x³y
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9. A man spends ₹x per week. The total money spent by him in xy² weeks is =
Money per week = ₹x
Number of weeks = xy²
Total spent = x × xy² =
x²y²
✔ Answer: ₹ x²y²
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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 number of girls =
g
According to problem:
> 4g + 3 = 47
Subtract 3 from both sides:
> 4g = 44
Divide by 4:
> g = 11
✔ Answer: 11 girls
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✔ Final Answers:
1.
5
2.
6s cm
3.
x⁴
4.
x³
5.
x²y
6.
18x⁵y⁵
7.
xy
8.
₹ x³y
9.
₹ x²y²
10.
11
You can fill these into the boxes on your worksheet! Let me know if you need help writing them out neatly. 😊
Parent Tip: Review the logic above to help your child master the concept of algebraic word problems worksheet.
