Q1. A number is tripled and then increased by 2 to equal 20. What is the number?
Solution:
Let the number be x. The equation is 3x + 2 = 20. Subtracting 2 gives 3x = 18, so x = 6.
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Q2. A number is increased by 5 and then multiplied by 3 to give 24. What is the number?
Solution:
Let the number be x. The equation is 3(x + 5) = 24. Simplifying gives 3x + 15 = 24. Subtract 15 from both sides: 3x = 9. Dividing by 3 gives x = 3.
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Q3. If 5 times a number is decreased by 2, the result is 18. What is the number?
Solution:
Let the number be x. Then, 5x - 2 = 18. Adding 2 to both sides gives 5x = 20. Dividing by 5 gives x = 4.
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Q4. If 4 times a number is increased by 6, the result is 30. What is the number?
Solution:
Let the number be x. Then, 4x + 6 = 30. Subtracting 6 from both sides gives 4x = 24. Dividing by 4 gives x = 6.
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Q5. A number is increased by 5 and then multiplied by 3. The result is 24. What is the number?
Solution:
Let the number be x. The equation is 3(x + 5) = 24. Simplifying gives 3x + 15 = 24. Subtracting 15 from both sides gives 3x = 9. Dividing by 3 gives x = 3.
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Q6. A number is subtracted from 15 and the result is 9. What is the number?
Solution:
Let the number be x. The equation is 15 - x = 9. Subtracting 15 from both sides gives -x = -6. Multiplying by -1 gives x = 6.
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Q7. A number decreased by 7 is equal to 3. What is the number?
Solution:
Let the number be x. The equation is x - 7 = 3. Adding 7 to both sides gives x = 10.
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Q8. If a number is multiplied by 3 and then increased by 9, the result is 30. What is the number?
Solution:
Let the number be x. The equation is 3x + 9 = 30. Subtracting 9 from both sides gives 3x = 21. Dividing by 3 gives x = 7.
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Q9. A rectangle's length is 3 times its width. If the perimeter is 48 cm, what is the width?
Solution:
Let the width be x. Then, length = 3x. The perimeter is 2(length + width) = 48. So, 2(3x + x) = 48. Simplifying gives 8x = 48, thus x = 6 cm.
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Q10. If a number is multiplied by 3 and then increased by 4, the result is 19. What is the number?
Solution:
Let the number be x. The equation is 3x + 4 = 19. Subtracting 4 gives 3x = 15, so x = 5.
