- Let Kara's age be \(n\).
- Cassie's age is \(2n - 3\).
- The total sum of their ages is 42, leading to the equation \(n + (2n - 3) = 42\).
- The blanks are filled as: \(n + (\boxed{2}n - \boxed{3}) = \boxed{42}\).
Explanation
- Defining Variables and Translating the Problem
Let \(n\) represent Kara's age. The problem states that Cassie's age is 3 less than twice Kara's age. We can express Cassie's age mathematically as \(2n - 3\). The sum of Kara's and Cassie's ages is given as 42. Therefore, the sum of their ages is the sum of \(n\) and \(2n - 3\).
- Formulating the Equation
We are given that the sum of their ages is 42. Combining the expression for Kara's age (\(n\)) and Cassie's age (\(2n - 3\)), we obtain the total sum:
\[n + (2n - 3) = 42\]
This matches the requested format:
\[n + (\boxed{2}n - \boxed{3}) = \boxed{42}\]
Examples
This type of problem helps in modeling real-world situations with algebraic equations. For example, if you are organizing a team where team members' experience levels depend on each other's, or managing resources that are related by a ratio and a constant offset, you can set up similar equations to determine individual values from a known total. Understanding how to translate word problems into equations is a fundamental skill in algebra that allows for solving complex resource allocation or scheduling tasks efficiently.