Solving percent problems generally involves understanding the relationship between a part, a whole, and the percentage. Here's a breakdown of common scenarios and how to solve them:
1. Finding a Percentage of a Whole
This is the most common type of percent problem. You are given a whole and a percentage, and you need to find the part.
Formula: Part = (Percentage / 100) * Whole
Example: What is 25% of 80?
- Percentage = 25
- Whole = 80
- Part = (25 / 100) 80 = 0.25 80 = 20
Therefore, 25% of 80 is 20.
2. Finding What Percentage One Number Is of Another
In this case, you are given the part and the whole, and you need to find the percentage.
Formula: Percentage = (Part / Whole) * 100
Example: What percentage of 50 is 10?
- Part = 10
- Whole = 50
- Percentage = (10 / 50) 100 = 0.2 100 = 20%
Therefore, 10 is 20% of 50.
3. Finding the Whole When You Know a Percentage of It
Here, you are given the part and the percentage, and you need to find the whole.
Formula: Whole = Part / (Percentage / 100)
Example: 15 is 30% of what number?
- Part = 15
- Percentage = 30
- Whole = 15 / (30 / 100) = 15 / 0.3 = 50
Therefore, 15 is 30% of 50.
Steps to Solve Any Percent Problem:
- Identify: Determine what you're trying to find (part, whole, or percentage).
- Write the formula: Choose the appropriate formula based on what you need to find.
- Substitute: Plug in the known values into the formula.
- Solve: Calculate the unknown value.
- Check: Make sure your answer makes sense in the context of the problem.
By understanding these basic types of percent problems and their corresponding formulas, you can confidently tackle a wide range of percentage-related calculations.
