Q1. The difference between twice a number and 4 is 10. What is the number?
Solution:
Let the number be x. The equation is 2x - 4 = 10. Adding 4 to both sides gives 2x = 14. Dividing by 2 gives x = 7.
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Q2. A rectangle's length is 3 times its width. If the perimeter is 48, what is the width?
Solution:
Let the width be w. Then the length is 3w. The perimeter is 2(w + 3w) = 48. Simplifying gives 8w = 48. Dividing by 8 gives w = 6.
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Q3. The difference between a number and 7 is 5. What is the number?
Solution:
Let the number be x. The equation is x - 7 = 5. Adding 7 to both sides gives x = 12.
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Q4. A number is divided by 2 and then increased by 3. The result is 10. What is the number?
Solution:
Let the number be x. Then, x/2 + 3 = 10. Subtracting 3 from both sides gives x/2 = 7. Multiplying by 2 gives x = 14.
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Q5. The difference between a number and 9 is 5. What is the number?
Solution:
Let the number be x. The equation is x - 9 = 5. Adding 9 gives x = 14.
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Q6. 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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Q7. A number is multiplied by 4 and then decreased by 8 to equal 16. What is the number?
Solution:
Let the number be x. The equation is 4x - 8 = 16. Adding 8 to both sides gives 4x = 24. Dividing by 4 gives x = 6.
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Q8. 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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Q9. If a number is multiplied by 4 and then increased by 8, the result is 32. What is the number?
Solution:
Let the number be x. Then, 4x + 8 = 32. Subtracting 8 from both sides gives 4x = 24. Dividing by 4 gives x = 6.
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Q10. 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.
