Q1. The sum of two numbers is 20, and their difference is 4. What are the two numbers?
Solution:
Let the two numbers be x and y. We have the equations: x + y = 20 and x - y = 4. Adding these gives 2x = 24, so x = 12. Substituting back gives y = 8.
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Q2. A number is increased by 25% and then decreased by 20%. If the final result is 96, what was the original number?
Solution:
Let the original number be x. The equation is: x * 1.25 * 0.8 = 96. Simplifying gives x = 96 / 1 = 120, so the original number is 100.
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Q3. Solve for x: 2x - 4 = 10.
Solution:
2x - 4 = 10. Add 4 to both sides: 2x = 14. Divide by 2: x = 7.
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Q4. If 5x + 2y = 20 and y = 2, what is the value of x?
Solution:
Substitute y = 2 into 5x + 2(2) = 20. This gives 5x + 4 = 20. Subtract 4: 5x = 16. Divide by 5: x = 16/5 = 3.2.
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Q5. Solve for y: 2y - 4 = 10.
Solution:
2y - 4 = 10. Add 4 to both sides: 2y = 14. Divide by 2: y = 7.
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Q6. If a rectangle has a length of 3x and a width of 2x, what is its area?
Solution:
Area = Length × Width = 3x × 2x = 6x^2.
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Q7. A rectangle has a length that is 3 times its width. If the perimeter of the rectangle is 48 cm, what is the width?
Solution:
Let the width be w cm. Then the length is 3w cm. The perimeter is given by: 2(length + width) = 48. Thus, 2(3w + w) = 48. Simplifying gives 8w = 48, so w = 6 cm.
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Q8. What is the solution to the equation 2(x - 3) = 4?
Solution:
2(x - 3) = 4. Divide by 2: x - 3 = 2. Add 3: x = 5.
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Q9. What is the solution to the inequality 2x + 5 > 15?
Solution:
2x + 5 > 15. Subtract 5 from both sides: 2x > 10. Divide by 2: x > 5.
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Q10. A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If a customer paid $70, how many miles did they drive?
Solution:
Let the number of miles driven be m. The total cost is given by: 50 + 0.20m = 70. Solving for m gives 0.20m = 20, so m = 100 miles.
