Problem 51 - Prealgebra

Question

The chart shows the heights of the three tallest buildings in the world. The height of the Empire State Building relative to the Petronas Towers can be given by the equation \(1483=233+x\). What is the height of the Empire State Building? (PICTURE NOT COPY)

Step-by-Step Solution

Answer

The height of the Empire State Building is 1250 feet.

Step 1: Understand the Equation

The equation given is \(1483 = 233 + x\). Here, \(1483\) represents the reference height (in feet) against which we are comparing. \(233\) is the known height of the Petronas Towers, and \(x\) is the unknown height of the Empire State Building.

Step 2: Isolate the Variable

To find the height of the Empire State Building, we need to solve for \(x\). We do this by isolating \(x\) on one side of the equation. The equation is: \(1483 = 233 + x\). Subtract \(233\) from both sides to get \(x = 1483 - 233\).

Step 3: Perform the Calculation

Perform the subtraction to solve for \(x\). Calculate \(1483 - 233\).

Step 4: Conclusion

After performing the calculation, the result is \(1483 - 233 = 1250\). Therefore, the height of the Empire State Building is \(1250\) feet.

Key Concepts

Algebraic Equations

Algebraic equations are mathematical statements that express the equality of two expressions.They often include variables, numbers, and operation signs. In our exercise, the equation is a simple one-step algebraic equation shown as \(1483 = 233 + x\).
This equation is set up to compare the heights of famous buildings. In this equation,

• \(1483\) is the total or combined height we're comparing against.
• \(233\) is a known value representing the height of the Petronas Towers.
• \(x\), the unknown, represents what we seek to find: the height of the Empire State Building.

For many algebraic equations, the goal is to find the unknown variable by manipulating the equation to a form where the variable is isolated.
This often involves basic arithmetic operations such as addition, subtraction, multiplication, or division.

Problem Solving

Problem solving within the context of algebraic equations involves multiple steps that lead us from a problem statement to a clear solution.Let's break it down using our original exercise. First, we carefully read and understand the problem. We identify what we know (e.g., the height of the Petronas Towers) and what we need to find out (e.g., the height of the Empire State Building).
Another important step is transforming a word problem or a description into a mathematical equation.This equation now serves as a tool to explore relationships between known and unknown values.
After setting up the equation, we can apply relevant mathematical techniques to solve for the unknown variable by isolating it.

• We begin by analyzing the given equation \(1483 = 233 + x\).
• Next, decide on the method—like subtraction—to isolate the variable \(x\).
• Finally, perform the computation and interpret the results. This gives the solution to our problem.

An effective problem-solving approach involves checking the solution by substituting it back into the original equation to verify its correctness.

Subtraction

Subtraction is one of the fundamental operations in mathematics. It helps us find the difference between numbers or remove a part of an overall amount.This operation is especially handy when working with algebraic equations to isolate variables.
In our original exercise, subtraction is used to simplify the equation and solve for \(x\). In the equation \(1483 = 233 + x\), our task is to find \(x\) by performing the subtraction \(1483 - 233\).
Here’s how subtraction is applied:

• Identify the terms you are working with. In this case, subtract \(233\) from \(1483\).
• Compute the difference: \(1483 - 233 = 1250\).
• The result, \(1250\), is the value of \(x\), representing the height of the Empire State Building.

Subtraction transforms complex mathematical expressions into simpler forms, enabling us to find solutions efficiently.