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Finding the Third Proportional to 97,977 and 146,586

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Solution

The third proportional to 97,977 and 146,586 is: 219,311.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    97,977 : 146,586 = 146,586 : x
  2. Step 2: Convert to fraction form
    97,977/146,586 = 146,586/x
  3. Step 3: Cross multiply
    97,977x = 146,586 × 146,586
  4. Step 4: Simplify right side
    97,977x = 21,487,455,396
  5. Step 5: Solve for x
    x = 21,487,455,396/97,977
  6. Step 6: Final answer
    x = 219,311.22

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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.