Question

Write an equation or an inequality to model the real-life situation. The distance \(s\) to school is \(\frac{1}{5}\) mile more than the distance \(c\) to the Community Center swimming pool.

Short answer

The equation to model the real-life situation is \(s = c + \frac{1}{5}\)

Step-by-step solution

Identify variables

From the problem, we can see that \(s\) represents the distance to school and \(c\) represents the distance to the Community Center swimming pool.

Set up equation from problem statement

The problem tells us that the distance to the school, \(s\), is 1/5 mile more than the distance to the swimming pool, \(c\). So, in mathematical terms, that can be translated to: \(s = c + \frac{1}{5}\)

Key concepts

Algebraic Expressions

Algebraic expressions are a cornerstone of algebra and provide a way to represent real-world situations with mathematical symbols and numbers. These expressions are made up of variables (like \( s \) and \( c \) in our example), constants, and operational symbols (such as +, -, \( \times \), and \( \div \)) that describe a particular quantity or set of relationships.

For instance, in the exercise above, the relationship between the distance to school (\( s \)) and the distance to the Community Center swimming pool (\( c \)) can be represented by the algebraic expression \( s = c + \frac{1}{5} \). Here, \( c \) is a variable representing an unknown quantity (the distance to the pool), while \( \frac{1}{5} \) is a constant that shows the fixed difference in distances.

Inequalities

Inequalities are similar to equations but instead of showing exact equality, they depict a relationship where one side is less than (<), greater than (>), less than or equal to (\( \leq \)), or greater than or equal to (\( \geq \)) the other. They are particularly useful for representing conditions or constraints in real-world problems, such as limits on resources, minimum requirements, or boundary conditions.

For example, if the problem stated that the distance to school was at least \( \frac{1}{5} \) mile more than the distance to the swimming pool, we would use an inequality: \( s \geq c + \frac{1}{5} \). This signifies that \( s \) could be exactly \( \frac{1}{5} \) mile more, or any distance greater than \( \frac{1}{5} \) mile more than \( c \).

Real-life Math Application

Applying math to real-life situations enables students to understand and appreciate the value of mathematical concepts in everyday life. The ability to write algebraic expressions and inequalities from real-life scenarios is a vital skill that can help solve problems ranging from personal finance to engineering challenges.

In our example, understanding the relationship between the distances to school and the Community Center swimming pool could help in planning the shortest route or estimating travel times. This illustration shows how algebra serves as a tool to model and solve practical problems with accuracy and efficiency, translating words into mathematical language that can be analyzed and solved.