Problem 58 - Algebra 1: Concepts and Skills

Question

In Exercises 58 and 59, use the table that shows the sizes (in acres) of the largest city parks in the United States. $$\begin{array}{|c|c|} \hline \text { Park (location) } & {\text { Size (acres) }} \\ \hline \text { Cullen Park (Houston, TX) } & {?} \\ \hline \text { Fairmount Park (Philadelphia, PA) } & {8700} \\ \hline \text { Griffith Park (Los Angeles, CA) } & {4218} \\ \hline \text { Eagle Creek Park (Indianapolis, IN) } & {?} \\ \hline \text { Pelham Bay Park (Bronx, NY) } & {2764} \\ \hline \end{array}$$ Griffith Park is 418 acres larger than Eagle Creek. Write an equation that models the size of Eagle Creek. Solve the equation to find the size of Eagle Creek Park.

Step-by-Step Solution

Answer

The size of Eagle Creek Park is \(3800\) acres.

Step 1: Analyze the provided data

From the problem, the size of Griffith Park: \(4218\) acres. Griffith Park is \(418\) acres larger than Eagle Creek Park.

Step 2: Formulate the equation

Let \(x\) be the size of Eagle Creek Park in acres. Based on given information the equation becomes: \(x + 418 = 4218\)

Step 3: Solve the equation

Solving for \(x\) gives the size of Eagle Creek Park: \(x = 4218 - 418\)

Step 4: Perform the calculation

Subtraction gives: \(x = 3800\) acres. So, the size of Eagle Creek Park is \(3800\) acres.

Key Concepts

Solving Linear Equations

Linear equations are like puzzles. They often show a straight relationship between two things. Usually, it's one plus or minus something equals the other. In the exercise provided, you were given the equation \(x + 418 = 4218\). Our job was to solve for \(x\) to find the answer.

Step-by-step, solving linear equations means finding the value of the unknown variable, which is \(x\) in this case. The main goal is to isolate \(x\). For our exercise, we moved 418 to the other side of the equals sign by subtracting 418 from 4218. This gives us \(x = 4218 - 418\).

Once you've isolated the variable on one side, you've solved the equation. This process is called 'solving for \(x\)'. Think of it as finding what number needs to go into the blank space to make the equation true.

Equation Formulation

Creating or formulating the right equation is the first step in solving any problem. It is just like setting a perfect scene in a puzzle. Let's take the provided problem as an example.

You know two things from the problem: the size of Griffith Park and that it is 418 acres larger than Eagle Creek Park. When formulating an equation, the key is to translate these words into math. For Eagle Creek Park, you started with an unknown size, \(x\). Because Griffith Park is 418 acres more than Eagle Creek, you expressed this relationship by \(x + 418 = 4218\).

In equation formulation, always look for words like "more than," "less than," "total," etc., to know what steps to take in forming the equation. These act as your clues.

Basic Arithmetic Operations

Arithmetic operations are the basic building blocks of maths, just like how words form a sentence. The four main operations are addition, subtraction, multiplication, and division. In our problem, we mainly used subtraction to solve for \(x\).

Once you have the linear equation set up, you use subtraction to isolate \(x\). From the equation \(x + 418 = 4218\), you subtract 418 from both sides to simplify it to \(x = 3800\). It is a straightforward calculation using basic arithmetic operations.

Understanding these operations and how to apply them to solve equations can make many math problems much easier. Always check your steps to ensure the arithmetic is correct, especially after solving an equation, to verify your solution.