Solving the Algebra Word Problem

This problem requires us to identify an unknown number using the information provided. We are told that if we take three times this number and then subtract 24 from the result, we get 258.

Translating the Problem into an Equation

Let's denote the unknown number as '$x$'. We can translate the sentence into a mathematical equation step-by-step:

• "Three times an unknown number" is represented as $3x$.
• "24 is subtracted from three times an unknown number" translates mathematically to $3x - 24$.
• The problem states that this difference "is 258".

Therefore, the equation we need to solve is:

$$3x - 24 = 258$$

Step-by-Step Solution

Our goal is to find the value of '$x$'. We can do this by isolating '$x$' on one side of the equation:

1. Isolate the term with '$x$': Add 24 to both sides of the equation to cancel out the subtraction. $$3x - 24 + 24 = 258 + 24$$ $$3x = 282$$
2. Solve for '$x$': Divide both sides by 3 to find the value of the unknown number. $$\frac{3x}{3} = \frac{282}{3}$$ $$x = 94$$

Verifying the Answer

To ensure the answer is correct, let's substitute $x = 94$ back into the original condition:

• Calculate three times the number: $3 \times 94 = 282$.
• Subtract 24 from the result: $282 - 24 = 258$.

Since the result is 258, which matches the value given in the problem, the unknown number is indeed 94.

Final Answer

The unknown number is 94.