Pair of Linear Equations - Word Problems for Competitive Exams

Pair of Linear Equations - Word Problems - Applications

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

A. 5
B. 19
C. 7
D. 12

Solution

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

Correct Answer: B — 19

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

A. 30
B. 15
C. 45
D. 60

Solution

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

Correct Answer: A — 30

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

A. 2w^2
B. w^2
C. 2w
D. w

Solution

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

Correct Answer: A — 2w^2

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

A. 60t
B. 60/t
C. t/60
D. t+60

Solution

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

Correct Answer: A — 60t

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

A. (x - 2)(x - 2)
B. (x + 2)(x + 2)
C. (x - 4)(x + 4)
D. (x + 4)(x - 4)

Solution

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

Correct Answer: A — (x - 2)(x - 2)

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

A. 15 - x
B. x + 15
C. x - 15
D. x/15

Solution

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

Correct Answer: A — 15 - x

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Q. If the sum of two numbers is 30 and one number is x, what is the other number?

A. 30 - x
B. x + 30
C. x - 30
D. x/30

Solution

Let the other number be y. Then x + y = 30. Therefore, y = 30 - x.

Correct Answer: A — 30 - x

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

A. 1
B. 2
C. 3
D. 4

Solution

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

Correct Answer: B — 2

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

A. 2
B. 3
C. 5
D. 10

Solution

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

Correct Answer: C — 5

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

A. x = 5
B. x = 1
C. x = 3
D. x = 2

Solution

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

Correct Answer: C — x = 3

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

A. x < 2
B. x > 2
C. x ≤ 2
D. x ≥ 2

Solution

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

Correct Answer: A — x < 2

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Pair of Linear Equations - Word Problems - Applications

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