- Represent Goran's age as \(g\).
- Identify "product of 18 and Goran's age" as \(18g\).
- Interpret "7 less than" as subtracting 7 from the product.
- Combine the components to get the expression \(\boxed{18g - 7}\).
Explanation
- Translating the Verbal Phrase into an Algebraic Expression
To translate the phrase "7 less than the product of 18 and Goran's age" into a mathematical expression, we break down the phrase into its components. First, we identify "Goran's age" as the variable \(g\). Second, "the product of 18 and Goran's age" means multiplying 18 by the variable \(g\), which is written as \(18g\). Finally, "7 less than" a certain quantity means we subtract 7 from that quantity. Therefore, "7 less than \(18g\)" is expressed as \(18g - 7\).
Examples
In real-life scenarios, algebraic expressions help us create models to solve problems quickly. For example, if a company charges an initial fee for a service plus a variable cost, we can represent this cost using an algebraic expression. Similarly, if Goran's age determines a fee for an activity, knowing this expression allows us to calculate the exact cost based on his age \(g\) by simply substituting the value of \(g\) into \(18g - 7\). Understanding how to build these expressions is a foundational skill in algebra.