What is 45 less than the product of 18 and a number written as an algebraic expression?
The problem asks us to translate a specific English phrase into an algebraic expression. Let the unknown number be denoted by the variable \(n\). We break the phrase "45 less than the product of 18 and a number" into smaller, manageable parts.
First, identify the "product of 18 and a number". In algebra, the word "product" indicates multiplication. Therefore, the product of 18 and \(n\) is written as \(18 \times n\) or simply \(18n\).
Next, consider the phrase "45 less than". This indicates that we need to subtract 45 from a base value. When we say "x less than Y", it mathematically represents the expression \(Y - x\). Applying this structure to our product, "45 less than \(18n\)" is written as \(18n - 45\).
Finally, we compare our derived expression, \(18n - 45\), with the given options. Our expression matches the first option: \(\boxed{18n - 45}\).
Algebraic expressions are the language of finance and everyday budgeting. For instance, if you are planning a birthday party and you know each guest costs \(\$18\) for food, but you have a \(\$45\) discount coupon for the total cost, you can represent the total cost of the party for \(n\) guests as \(18n - 45\). Being able to translate these real-world scenarios into math helps you model costs and make smarter planning decisions!