Pair of Linear Equations - Word Problems

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Q1. A number is increased by 15 and the result is 45. What is the number?

Solution:

Let the number be x. Then x + 15 = 45. Subtract 15 from both sides: x = 30.

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Q2. What is the solution to the equation 3(x - 1) = 2(x + 2)?

Solution:

3(x - 1) = 2(x + 2). Expanding gives 3x - 3 = 2x + 4. Subtract 2x: x - 3 = 4. Add 3: x = 7.

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Q3. Solve for y: 2y - 3 = 7.

Solution:

2y - 3 = 7. Add 3 to both sides: 2y = 10. Divide by 2: y = 5.

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Q4. What is the solution to the inequality 4x - 8 < 0?

Solution:

4x - 8 < 0. Add 8 to both sides: 4x < 8. Divide by 4: x < 2.

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Q5. If a polynomial is given by P(x) = x^2 - 4x + 4, what is its factored form?

Solution:

P(x) = x^2 - 4x + 4 = (x - 2)(x - 2) or (x - 2)^2.

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Q6. A train travels 60 km in 1 hour. How far will it travel in t hours?

Solution:

Distance = Speed × Time. Therefore, Distance = 60 km/h × t h = 60t km.

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Q7. A rectangle has a length that is twice its width. If the width is w, what is the area of the rectangle?

Solution:

Area = Length × Width. Length = 2w, so Area = 2w × w = 2w^2.

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Q8. If the sum of two numbers is 15 and one number is x, what is the other number?

Solution:

Let the other number be y. Then x + y = 15. Therefore, y = 15 - x.

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Q9. Solve for x: 2x - 3 = 5.

Solution:

2x - 3 = 5. Add 3 to both sides: 2x = 8. Divide by 2: x = 4.

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Q10. A number decreased by 7 equals 12. What is the number?

Solution:

Let the number be x. Then x - 7 = 12. Add 7 to both sides: x = 19.