If a number is multiplied by 9 and then decreased by 27, the result is 54. What

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Question: If a number is multiplied by 9 and then decreased by 27, the result is 54. What is the number?

Options:

Correct Answer: 6

Solution:

Let the number be x. Then, 9x - 27 = 54. Solving gives x = 9.

If a number is multiplied by 9 and then decreased by 27, the result is 54. What is the number?

If a number is multiplied by 9 and then decreased by 27, the result is 54. What is the number?

Step 1: Let's call the unknown number 'x'.
Step 2: According to the problem, if we multiply 'x' by 9, we write it as 9x.
Step 3: After multiplying by 9, we decrease the result by 27. This gives us the equation: 9x - 27.
Step 4: The problem states that this result equals 54. So we write the equation: 9x - 27 = 54.
Step 5: To solve for 'x', we first add 27 to both sides of the equation: 9x - 27 + 27 = 54 + 27.
Step 6: This simplifies to: 9x = 81.
Step 7: Now, we divide both sides by 9 to find 'x': 9x / 9 = 81 / 9.
Step 8: This simplifies to: x = 9.

Algebraic Equations – The question tests the ability to set up and solve a linear equation based on a word problem.
Order of Operations – Understanding the sequence of operations when manipulating the equation.