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Finding the Third Proportional to 31,407 and 75,897

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Solution

The third proportional to 31,407 and 75,897 is: 183,409.90

Step by Step Solution

  1. Step 1: Write the proportion equation
    31,407 : 75,897 = 75,897 : x
  2. Step 2: Convert to fraction form
    31,407/75,897 = 75,897/x
  3. Step 3: Cross multiply
    31,407x = 75,897 × 75,897
  4. Step 4: Simplify right side
    31,407x = 5,760,354,609
  5. Step 5: Solve for x
    x = 5,760,354,609/31,407
  6. Step 6: Final answer
    x = 183,409.90

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Why These Related Problems?

These problems maintain the same ratio (2.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.