Karen and Clarann's Music Library Playlists

Problem Overview

• Subject: Solving a problem involving the number of playlists in two music libraries.
• Participants: Karen and Clarann.
• Information Given:
  • Karen has 18 more playlists than Clarann.
  • The total number of playlists in both libraries combined is 68.

Problem Breakdown

Known Variables

• Let the number of playlists in Clarann's library be denoted as C.
• Therefore, the number of playlists in Karen's library can be expressed as K = C + 18.

Total Playlists Equation

• The total number of playlists in both libraries is given by the equation:
  • $K + C = 68$

Substituting for K

• By substituting Karen's equation into the total playlists equation:
  • $(C + 18) + C = 68$

Simplifying the Equation

• Combining like terms gives:
  • $2C + 18 = 68$

Solving for C

• Step 1: Subtract 18 from both sides of the equation:
  • $2C = 68 - 18$
• Step 2: Simplify the right side:
  • $2C = 50$
• Step 3: Divide both sides by 2 to find C:
  • $C = \frac{50}{2} = 25$

Finding K

• Substitute C back into Karen's equation to find K:
  • $K = C + 18$
  • $K = 25 + 18$
  • $K = 43$

Conclusion

• The number of playlists in each person's music library is:
  • Clarann's music library: 25 playlists
  • Karen's music library: 43 playlists

Visual Representation

• The problem-solving flowchart can be structured as:
  • Start with the total: 68 playlists
  • Identify the difference: +18 (Karen has more)
  • Set equations based on the variables defined: 2C + 18 = 68
  • Solve incrementally until both results are known.

Final Note

• Ensure to double-check calculations for accuracy with:
  • Total playlists: $K + C = 43 + 25 = 68$.