Solving a Fraction Word Problem Using a Linear Equation

Problem Statement

• Context: Isabelle needs to memorize words on a vocabulary list for Korean class.
• Given:
  • Isabelle has memorized 20 words.
  • These 20 words represent 1/4 of the total list.
• Objective: Find out how many words are in the complete list.

Approach

1. Understanding the Equation:

   • The phrase "which is" indicates an equation setup. Here, it leads to the equation:
     • 20 = 1/4 * x
   • x represents the total number of words in the list.

2. Solving the Equation:

   • To isolate x, multiply both sides of the equation by the reciprocal of 1/4, which is 4.
   • The modified equation becomes:
     • 4 * 20 = x
   • Simplifying:
     • 80 = x

3. Verification:

   • Check if the solution makes sense:
     • If 20 words are 1/4 of the total, then multiplying 20 by 4 confirms that the list should contain 80 words.

Conclusion

• Total Words in List: 80
• Verification Conclusion: The calculation and reasoning align, confirming the list should indeed have 80 words.