Finding the Number: Solving a Simple Word Problem

The question asks us to find a specific number. We are given a condition about this number: its value when multiplied by 6 is equal to a value that is 6 less than 60.

Let's represent the unknown number with a variable. A common variable used in algebra is \(x\).

According to the problem statement, we can set up an equation:

• "6 times the number" can be written as \(6 \times x\) or simply \(6x\).
• "6 less than 60" means we subtract 6 from 60, which is \(60 - 6\).
• The problem states that these two quantities are equal.

So, the equation that represents the problem is:

\[6x = 60 - 6\]

Solving the Equation to Find the Number

Now, we need to solve this linear equation for \(x\).

First, simplify the right side of the equation:

\[60 - 6 = 54\]

So the equation becomes:

\[6x = 54\]

To find the value of \(x\), we need to isolate \(x\) on one side of the equation. Since \(x\) is multiplied by 6, we perform the inverse operation, which is division. We divide both sides of the equation by 6:

\[\frac{6x}{6} = \frac{54}{6}\]

Simplifying both sides gives us:

\[x = 9\]

So, the number is 9.

Verifying the Solution

Let's check if our answer, \(x = 9\), satisfies the original condition:

• 6 times the number: \(6 \times 9 = 54\).
• 6 less than 60: \(60 - 6 = 54\).

Since \(54 = 54\), our solution is correct. The number whose 6 times is 6 less than 60 is indeed 9.

Matching the Answer with Options

Now, let's compare our answer to the given options:

• A. 6
• B. 7
• C. 8
• D. 9

Our calculated number is 9, which matches option D.

The final answer is the number 9.

Revision Table: Key Concepts

Additional Information: Translating Word Problems

Translating word problems into mathematical equations is a crucial skill in algebra. Here are some common phrases and their mathematical equivalents:

• "a number": Use a variable, like \(x\) or \(n\).
• "is", "equals", "is equal to": Represented by the equals sign (\(=\)).
• "sum of", "increased by", "more than": Addition (\(+\)).
• "difference between", "decreased by", "less than": Subtraction (\(-\)). Be careful with the order in "less than" (e.g., "6 less than 60" is \(60 - 6\), not \(6 - 60\)).
• "product of", "times", "multiplied by": Multiplication (\(\times\) or just putting terms next to each other, like \(6x\)).
• "quotient of", "divided by": Division (\(\div\) or fraction bar).

Practicing translating different phrases will help you set up equations correctly and solve word problems efficiently.