Math Antics: Solving for the 'Total' in Percent Problems

Introduction

• In previous lessons, we covered solving for the 'part' and the 'percent' in percent problems.
• This lesson focuses on solving for the 'total'.
• The percentage equation involves three main numbers: the 'part', the 'total', and the 'percent', with the constant 100.

Solving for the 'Total'

• You need to find the 'total' when it is unknown.
• You will be given:
  • The 'percent' value.
  • The 'part' value of the total.

Example 1: Marbles Problem

• Problem: Your friend has a bag of marbles, with 20% being red. There are 7 red marbles. Find the total number of marbles.
• Clues for identifying the missing number:
  • Words like "altogether", "in all", "total", "whole", "entire" suggest finding the 'total'.
  • Given numbers: 'percent' = 20, 'part' = 7
• Steps to solve:
  1. Multiply the 'part' by 100: 7 × 100 = 700
  2. Divide the result by the 'percent': 700 ÷ 20 = 35
• Conclusion: Total number of marbles = 35
• Verification: Ensure fraction of 'part' over 'total' gives the correct 'percent'.

Example 2: Marching Band Problem

• Problem: A high school marching band has 12 flute players, making up 8% of the band. Find the total number of band members.
• Given numbers: 'part' = 12, 'percent' = 8
• Steps to solve:
  1. Multiply the 'part' by 100: 12 × 100 = 1,200
  2. Divide by the 'percent': 1,200 ÷ 8 = 150
• Conclusion: Total number of band members = 150
• Verification: Check calculation as in the previous example.

Conclusion

• Practice solving percent problems by identifying which number is missing.
• Master the two-step process to find the 'total'.
• Practicing on your own will enhance problem-solving skills.
• For more resources, visit Math Antics.