- Translate the sentence to the equation \(3n - 15 = 36\).
- Analyze Statement A: Matches the subtraction of 15 from the product \(3n\). (True)
- Analyze Statement B: Suggests subtracting 15 from 3, which is incorrect. (False)
- Analyze Statement C and D: Both correctly describe the equation's components. (True)
- The incorrect statement is \(\boxed{B}\).
Explanation
- Translating the Sentence to an Equation
The problem states: "Fifteen less than the product of three and a number is thirty-six." To analyze this, we define a variable \(n\) to represent the unknown number.
- "The product of three and a number" translates to \(3n\).
- "Fifteen less than the product of three and a number" means we subtract 15 from the product: \(3n - 15\).
- "is thirty-six" represents the equality: \(3n - 15 = 36\).
This gives us the complete mathematical equation: \(3n - 15 = 36\). We will use this to evaluate the given statements.
- Evaluating the Statements
We evaluate each provided statement based on our translated equation \(3n - 15 = 36\):
- A. "Fifteen is subtracted from the result after multiplying."
This describes the expression \(3n - 15\), where the product \(3n\) is calculated first, and then 15 is subtracted. This statement is true.
- B. "Fifteen is subtracted from 3."
This would be represented as \(3 - 15\). Our expression is \(3n - 15\), meaning 15 is subtracted from the product \(3n\), not from the number 3. This statement is false.
- C. "The final result is 36."
The sentence explicitly ends with "is thirty-six", implying that the result of the entire expression is 36. This statement is true.
- D. "The unknown number is multiplied by 3."
Our expression includes \(3n\), which is the result of multiplying the number \(n\) by 3. This statement is true.
- Conclusion
After carefully evaluating each option against the mathematical translation of the problem, we have determined that statements A, C, and D accurately describe components of the equation \(3n - 15 = 36\). Statement B, which claims that 15 is subtracted from 3, does not reflect the mathematical structure of the sentence. Therefore, statement B is the incorrect one. The final answer is B.
Examples
In algebra, translating word problems into mathematical expressions is a critical skill for solving real-world problems. For example, if a store owner knows that "triple the number of sales today minus fifteen, you get thirty-six total items left," they can set up the equation \(3n - 15 = 36\) to solve for the number of items sold (\(n\)). Understanding how to correctly parse these phrases, such as distinguishing between subtracting from a constant versus subtracting from a variable product, is essential for accurate modeling.