105 Is 35 Of What Number

105 is 35% of What Number? Solving Percentage Problems

This article will guide you through solving the percentage problem: "105 is 35% of what number?" We'll break down the process step-by-step, offering multiple approaches so you can choose the method that best suits your understanding. Understanding how to solve percentage problems is crucial for various applications, from everyday budgeting to more complex mathematical calculations.

Understanding the Problem

The question, "105 is 35% of what number?", is essentially asking us to find the original whole number from which 35% equates to 105. We can represent this problem algebraically:

• Let 'x' represent the unknown number.
• The problem translates to the equation: 0.35x = 105

Method 1: Algebraic Solution

This method utilizes basic algebra to solve for the unknown variable 'x'.

1. Set up the equation: 0.35x = 105
2. Isolate 'x': To isolate 'x', divide both sides of the equation by 0.35: x = 105 / 0.35
3. Calculate 'x': Performing the division, we find that x = 300

Therefore, 105 is 35% of 300.

Method 2: Using Proportions

Proportions offer a visual and intuitive way to solve percentage problems. We can set up a proportion as follows:

• 35/100 = 105/x

This proportion states that the ratio of 35 to 100 (representing 35%) is equal to the ratio of 105 to the unknown number (x).

1. Cross-multiply: Multiply the numerator of one fraction by the denominator of the other and vice versa: 35x = 105 * 100
2. Simplify: This simplifies to 35x = 10500
3. Solve for 'x': Divide both sides by 35: x = 10500 / 35
4. Calculate 'x': This gives us x = 300

Again, we find that 105 is 35% of 300.

Method 3: Using the Percentage Formula

The basic percentage formula is: (Part / Whole) * 100 = Percentage

In our case, we know the "Part" (105) and the "Percentage" (35%). We need to find the "Whole". Let's rearrange the formula:

Whole = (Part / Percentage) * 100

1. Substitute values: Whole = (105 / 35) * 100
2. Calculate: Whole = 3 * 100 = 300

This confirms that 105 is 35% of 300.

Practical Applications

Understanding how to solve percentage problems has many real-world applications:

• Calculating discounts: Determining the original price of an item after a percentage discount.
• Analyzing financial data: Interpreting financial statements and growth rates.
• Determining tax amounts: Calculating sales tax or income tax.
• Understanding statistics: Interpreting survey results and statistical data.

By mastering these methods, you'll be well-equipped to tackle various percentage problems with confidence. Remember to choose the method you find most comfortable and apply it consistently for accurate results. Practice is key to becoming proficient in solving percentage problems.