Verified Answer :

  • The phrase "three times a number" translates mathematically to the product of 3 and a variable \(x\), written as \(3x\).
  • This expression represents the repeated addition of the quantity \(x\), effectively \(x + x + x\).
  • Comparing the given options, the second choice, \(3x\), is the only one that correctly translates the verbal phrase into an algebraic expression and provides a visual model of three instances of \(x\).
  • The final answer is \(\boxed{3x}\).

Explanation

  1. Mathematical Translation of the Phrase

The mathematical expression "three times a number" translates the phrase into a product. A "number" is represented by a variable, typically \(x\). "Three times" indicates multiplication by 3. Therefore, "three times a number" corresponds to the algebraic expression \(3 \times x\), or simply \(3x\). This expression signifies that the quantity \(x\) is being taken or added together three separate times, i.e., \(x + x + x = 3x\).

  1. Evaluation of the Options

We must choose the representation that correctly matches the expression \(3x\) and shows a visual configuration corresponding to this meaning.

  • The expression \(3+x\) represents "three added to a number", not "three times a number".
  • The expression \(x+3\) represents "a number plus three", also not "three times a number".
  • The expression \(3x\) correctly represents "three times a number". Looking at the provided options, the second option clearly presents the expression \(3x\) accompanied by a visual stack of three \(x\)'s. This stack effectively illustrates the repeated addition of the value \(x\), which is a standard conceptual model for multiplication.
  1. Conclusion

The correct mathematical representation of "three times a number" is \(3x\). The visual diagram representing this as a sum of three individual quantities of \(x\) (i.e., \(x+x+x\)) confirms that the second option is the intended answer. The symbols \(\rightarrow\), \(\Rightarrow\), or \(\longrightarrow\) in the other options are part of the labeling, but the core mathematical content of the second option is the only one that is both algebraically correct and conceptually supported by the diagram.

Examples

Think of a bakery where you buy boxes of donuts. If each box contains \(x\) donuts, and you decide to buy 3 boxes, the total number of donuts you have is "three times the number of donuts in a box," which is \(3x\). If you put all the boxes on a shelf, you see the first box (\(x\)), the second box (\(x\)), and the third box (\(x\)), which confirms the representation of \(3x\) as \(x + x + x\). Understanding this helps in calculating total quantities of items in real-world situations.

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