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Finding the Third Proportional to 123,144 and 198,324

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Solution

The third proportional to 123,144 and 198,324 is: 319,401.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    123,144 : 198,324 = 198,324 : x
  2. Step 2: Convert to fraction form
    123,144/198,324 = 198,324/x
  3. Step 3: Cross multiply
    123,144x = 198,324 × 198,324
  4. Step 4: Simplify right side
    123,144x = 39,332,408,976
  5. Step 5: Solve for x
    x = 39,332,408,976/123,144
  6. Step 6: Final answer
    x = 319,401.75

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Why These Related Problems?

These problems maintain the same ratio (1.61) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.