- Translate 'the product of a number and 5' to \(5y\).
- Add 8 to the product to account for 'eight more than', resulting in \(5y + 8\).
- Relate the expression to 9 using the equality symbol 'is'.
- The final equation is \(\boxed{5y + 8 = 9}\).
Explanation
- Translating the Statement into an Equation
We need to translate the verbal statement 'Eight more than the product of a number and 5 is 9' into a mathematical equation using the variable \(y\) to represent the unknown number. We break the statement down into mathematical components. First, the 'product of a number and 5' is represented as \(5y\). Second, 'eight more than' this product corresponds to adding 8, yielding \(5y + 8\). Finally, the word 'is' denotes equality, leading us to set this expression equal to 9.
- Formulating the Final Equation
By combining the components identified in the previous step, we obtain the final equation:
\[5y + 8 = 9.\]
This equation captures the relationship described in the original problem statement.
Examples
Algebraic translation is a foundational skill in mathematics used to represent real-world scenarios as equations. For example, if you know that a taxi fare consists of a fixed base fee of \(\$8\) plus \(\$5\) for every mile driven, and you want to find how many miles \(y\) you can travel for exactly \(\$9\), you would model this situation with the equation \(5y + 8 = 9\). Solving this equation allows you to determine the specific distance you can afford, demonstrating how translation bridges descriptive language and quantitative problem-solving.