Question

Translate to an equation and solve. What percent is 114 out of \(200 ?\)

Short answer

Answer: 57%

Step-by-step solution

Understand the problem

We want to find out what percent 114 is out of 200.

Set up the equation

In order to find the percentage, we can set up the equation: \(\frac{114}{200} = \frac{x}{100}\), where x is the percentage we want to find.

Solve for x

Multiply both sides of the equation by 100 to isolate x: \(x = \frac{114}{200} \cdot 100\).

Calculate the percentage

Now we can calculate the percentage by dividing 114 by 200 and multiplying by 100: \(x = \frac{114}{200} \cdot 100 = 57\). So, 114 is 57% of 200.

Key concepts

Understanding Equations

Equations are mathematical statements that assert the equality of two expressions. They are fundamental tools in algebra and calculus, allowing us to solve for unknown variables. In this problem, we are given the fraction of 114 out of 200 and are asked to find the percentage it represents. An equation is set up to represent this problem: \[\frac{114}{200} = \frac{x}{100} \]This equation is based on the concept that a percentage is simply a fraction with a denominator of 100.
Equations are solved through operations that maintain balance on both sides. When dealing with percentages, remember that multiplying fractions or ratios by 100 converts them into percentages. This is because percentages are standardized to "per one hundred" units.

Working with Fractions

Fractions represent a part of a whole and are used everywhere in math problems, especially involving division or sharing. Here, the fraction \(\frac{114}{200}\) represents 114 out of 200 total, which we will convert into a percentage. To do this, we use an equation to set this fraction equal to another fraction \(\frac{x}{100}\), where 100 represents the whole as percentage typically does.

• The numerator (114) is the part of the total you are focusing on.
• The denominator (200) is the total or the whole quantity.
• Fractions like this are the first step in converting values to percentages.

Solving involves converting the fraction into a percentage by multiplying the top number (numerator) by 100 and then dividing by the bottom number (denominator):\[x = \frac{114}{200} \cdot 100\] This results in the percentage representation.

Steps in Problem Solving

Problem solving often involves breaking down a complex problem into manageable steps, just like we did with our percent problem. It's crucial to:

• Understand the question - "What percent is one number of another?" means finding the fraction and converting it to a percentage.
• Set up your solution - Use an equation to represent the problem.
• Solve the equation - Perform operations that simplify and solve for the unknown.
• Verify the result - Ensuring that the percentage makes sense in the context of the problem helps confirm accuracy.

Each of these steps builds on the other, leading from understanding the problem to calculating a solution. When tackling percentage problems, remember that setting up the right equation is key. Once set, operations like multiplying by 100 make the final conversion smooth and efficient. Practice these steps to make problem solving easier and more intuitive.