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A number is increased by 5 and then multiplied by 3. The result is 24. What is t

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Question: A number is increased by 5 and then multiplied by 3. The result is 24. What is the number?

Options:

  1. 1
  2. 3
  3. 5
  4. 7

Correct Answer: 3

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.

A number is increased by 5 and then multiplied by 3. The result is 24. What is t

Practice Questions

Q1
A number is increased by 5 and then multiplied by 3. The result is 24. What is the number?
  1. 1
  2. 3
  3. 5
  4. 7

Questions & Step-by-Step Solutions

A number is increased by 5 and then multiplied by 3. The result is 24. What is the number?
  • Step 1: Let the unknown number be represented by 'x'.
  • Step 2: According to the problem, we first increase 'x' by 5. This can be written as 'x + 5'.
  • Step 3: Next, we multiply the result from Step 2 by 3. This gives us '3(x + 5)'.
  • Step 4: We know that this result equals 24, so we can write the equation: 3(x + 5) = 24.
  • Step 5: Now, we simplify the left side of the equation. Distributing 3 gives us: 3x + 15 = 24.
  • Step 6: To isolate '3x', we need to get rid of the 15. We do this by subtracting 15 from both sides of the equation: 3x + 15 - 15 = 24 - 15.
  • Step 7: This simplifies to: 3x = 9.
  • Step 8: Now, we need to find 'x'. We do this by dividing both sides of the equation by 3: 3x / 3 = 9 / 3.
  • Step 9: This gives us the final answer: x = 3.
  • Algebraic Manipulation – The question tests the ability to set up and solve a linear equation based on a verbal description of a mathematical operation.
  • Order of Operations – Understanding the sequence of operations (addition before multiplication) is crucial for correctly forming the equation.
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