Problem 61 - Algebra 1: Concepts and Skills

Question

Solve the percent problem. 105 is what percent of \(240 ?\)

Step-by-Step Solution

Answer

105 is approximately \(43.75\%\) of 240. The calculation leads to this conclusion.

Step 1: Identify the Values

From the question, it is clear that the part is 105 (represented as 'Part') and the whole is 240 (represented as 'Whole').

Step 2: Setting up the Formula

The next step would involve putting the numbers into the formula: \((Part/Whole)*100\). This will result in \((105/240)*100.\)

Step 3: Solving the Calculation

To solve this, divide 105 by 240 and then multiply the result by 100. The quotient obtained is the percentage value.

Key Concepts

Understanding Percentage Calculation

Calculating percentages is an essential mathematical skill that helps quantify relationships between parts and wholes. To find what percentage 105 is of 240, we use a simple formula:

• Identify the part and the whole. Here, 105 is the "part," and 240 is the "whole."
• Use the formula to find the percentage: \[ \frac{\text{Part}}{\text{Whole}} \times 100 \]
• Apply the numbers: \[ \frac{105}{240} \times 100 \]

This formula helps us understand how one amount relates to another as a percentage. The resulting percentage shows how much the part represents of the whole. Breaking calculations down into these steps can facilitate a clearer understanding of both the process and the result.

Basic Algebra in Percentage Problems

Algebraic thinking is crucial when solving percentage problems! Algebra helps organize calculations and solve problems efficiently by using formulas. First, transpose word problems into mathematical expressions or equations. With the example given, we were asked to find the percentage:

• Set the equation with fractions: \[ x = \frac{105}{240} \]
• "x" is the unknown, representing the percentage when multiplied by 100.

Algebra allows us to systematically substitute values, isolating variables like "x," making solving easier. Identify the operations needed (division and multiplication, in this case), then perform them step-by-step. This structure enhances comprehension and provides a reliable method for solving many similar mathematical problems.

Mathematical Formulas as Problem-Solving Tools

Mathematical formulas are powerful tools for solving problems quickly and precisely. The formula for calculating percentages, \[ \frac{\text{Part}}{\text{Whole}} \times 100 \], serves as a universal tool applicable to many contexts, such as finance, statistics, and general problem-solving.

Key Benefits

• Simplifies Complex Calculations: By plugging values into a formula, you streamline complex calculations into straightforward operations.
• Consistency and Accuracy: Formulas ensure consistent and accurate results across different problems by following set procedures.
• Versatility: Whether calculating discounts, growth rates, or comparisons, formulas like this ensure you understand and can solve diverse percentage-related problems.

Mastering mathematical formulas boosts confidence in your ability to tackle a wide array of tasks efficiently. Embrace them as essential tools in your math toolkit!