Problem 32 - Prealgebra

Question

A forest preserve rents canoes for \(\$ 12\) per hour. Corey has \(\$ 36\). Write and solve an equation to find how many hours he can rent a canoe.

Step-by-Step Solution

Answer

Corey can rent a canoe for 3 hours.

Step 1: Understanding the Problem

We know that the cost to rent a canoe is $12 per hour, and Corey has $36 available. We need to find out how many hours 'h' he can rent the canoe.

Step 2: Setting Up the Equation

The total cost of renting a canoe for 'h' hours is 12 times 'h'. This total cost should equal 36 dollars, the amount Corey has. Therefore, the equation is: \( 12h = 36 \).

Step 3: Solving the Equation

To solve for 'h', divide both sides of the equation by 12 to isolate the variable 'h'. This gives: \( h = \frac{36}{12} \).

Step 4: Simplifying the Equation

Simplify the right side of the equation: \( \frac{36}{12} = 3 \).

Key Concepts

Understanding Word Problems

Word problems in mathematics pull scenarios from everyday life and ask students to build and solve equations based on the information provided. These problems help bridge the gap between abstract numerical calculations and real-world applications. The key to solving word problems is to thoroughly comprehend the situation described. Ask yourself questions like: What are we solving for? What information has been provided? What do the numbers represent in this context? For instance, in the canoe rental problem, we know the rate per hour and the total amount Corey has, making it easier to form and solve the equation. By breaking down the problem into manageable parts, you effectively organize your thoughts, making it easier to find the solution.

Solving for a Variable

Solving for a variable involves finding the value of the unknown, often represented by a letter like 'h' in an equation. To solve for a variable, one must isolate it to one side of the equation.

Here are the steps:

• Identify the equation you need to solve. In our example, it's: \(12h = 36\).
• Use inverse operations to isolate the variable. For Corey’s problem, divide each side of the equation by 12.
• Verify your solution by substituting the variable back into the original context. In this case, plugging '3' back into the equation confirms that Corey can rent the canoe for 3 hours.

Creating and solving algebraic equations not only helps determine unknown quantities but also enhances strategic thinking and problem-solving skills.

Importance of Mathematics Education

Mathematics education is crucial in developing logical thinking and problem-solving skills. Activities like solving algebraic equations through word problems help improve analytical thinking and the ability to apply mathematical concepts to real-world scenarios.

The benefits of learning mathematics include:

• Improved decision-making skills.
• Enhanced analytical and logical reasoning abilities.
• The development of critical thinking skills through pattern recognition and problem-solving.

By incorporating these skills in everyday situations, students not only prepare for academic success but also equip themselves to face life’s challenges with confidence and competence. Word problems, like the canoe rental scenario, enable students to see mathematics as a tool to answer practical questions and make informed decisions.