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Finding the Third Proportional to 65,537 and 98,223

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Solution

The third proportional to 65,537 and 98,223 is: 147,210.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    65,537 : 98,223 = 98,223 : x
  2. Step 2: Convert to fraction form
    65,537/98,223 = 98,223/x
  3. Step 3: Cross multiply
    65,537x = 98,223 × 98,223
  4. Step 4: Simplify right side
    65,537x = 9,647,757,729
  5. Step 5: Solve for x
    x = 9,647,757,729/65,537
  6. Step 6: Final answer
    x = 147,210.85

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.