- Identify the variable \(g\) as Gail's height.
- Translate "24 more than" to the expression \(g + 24\).
- Translate "is 58" as the equation component \(= 58\).
- Combine the expressions to form the final equation: \(\boxed{g + 24 = 58}\).
Explanation
- Problem Analysis and Variable Identification
We are given a sentence to translate into a mathematical equation: "24 more than Gail's height is 58." We are instructed to use the variable \(g\) to represent Gail's height. Our task is to represent the relationship described in the sentence using algebraic notation.
- Translating Phrases into Algebraic Expressions
The phrase "24 more than Gail's height" involves the variable \(g\). The word "more than" implies an addition operation. Therefore, "24 more than Gail's height" is expressed as the sum of Gail's height, \(g\), and 24, which is \(g + 24\). The word "is" in mathematical statements indicates equality. Thus, "is 58" is represented as \(= 58\).
- Formulating the Equation and Conclusion
By combining these parts, we equate the expression for "24 more than Gail's height" to 58. Combining \(g + 24\) and \(= 58\), we obtain the equation \(g + 24 = 58\). This equation accurately represents the given sentence using the variable \(g\).
Examples
In everyday life, algebra is used to represent real-world relationships. For example, if you know the price of a standard cinema ticket is \(\$12\) and a special premium ticket costs \(\$5\) more, you can write an equation where \(p\) is the standard price: \(p + 5 = \text{premium price}\). This simple translation helps organize information to solve for unknown values in various planning or budgeting scenarios.