Lecture Notes: Solving Percent Problems Using Proportions

Introduction to Percent Proportions

• Percent Proportion: A method used to determine the percent of a number.
  • Compares the part and the whole to a percent over 100.
  • Part: Number being compared to the whole.
  • Whole: Total quantity or number to which the part is compared.
• Real-Life Applications:
  • Shopping: Taxes, tips, and discounts.
  • Commission: Percentages in sales (e.g., buying a car).

Understanding Percent Proportions

• Equation Structure: Is/Of = Part/Whole = Percent/100.
  • Helps in reading word problems.
• Example 1: Finding the percent of students playing a brass instrument in a band.
  • Given: 9 out of 24 students play a brass instrument.
  • Setup: 9/24 = x/100.

Solving Different Types of Percent Problems

Finding the Percent

• Example: What percent of 150 is 45?
  • Rewrite: 45/150 = x/100.
  • Solve for x to find 30%.

Finding the Part

• Example: 30% of 150 is what number?
  • Rewrite: x/150 = 30/100.
  • Solve for x to find the part.

Finding the Whole

• Example: 30% of what number is 45?
  • Rewrite: 45/x = 30/100.
  • Solve for x to find the whole.

Application Example

• Problem: Sale price of Air Jordan shoes is $120, which is 75% of the original price.
  • Setup: 120 = 75/100 * x.
  • Solve for x to find the original price $160.*

Summary

• Percent proportions can solve various percent problems.
  • Finding the part: E.g., 60% of 50 is what number?
  • Finding the whole: E.g., 60% of what number is 30?
  • Finding the percent: E.g., what percent of 50 is 30?
• Key Takeaway: Understanding percent proportions is sufficient for solving all types of percent problems efficiently.

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