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Finding the Third Proportional to 27,097 and 39,598

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Solution

The third proportional to 27,097 and 39,598 is: 57,866.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    27,097 : 39,598 = 39,598 : x
  2. Step 2: Convert to fraction form
    27,097/39,598 = 39,598/x
  3. Step 3: Cross multiply
    27,097x = 39,598 × 39,598
  4. Step 4: Simplify right side
    27,097x = 1,568,001,604
  5. Step 5: Solve for x
    x = 1,568,001,604/27,097
  6. Step 6: Final answer
    x = 57,866.24

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Why These Related Problems?

These problems maintain the same ratio (1.46) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.