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Finding the Third Proportional to 257,712 and 409,992

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Solution

The third proportional to 257,712 and 409,992 is: 652,253.06

Step by Step Solution

  1. Step 1: Write the proportion equation
    257,712 : 409,992 = 409,992 : x
  2. Step 2: Convert to fraction form
    257,712/409,992 = 409,992/x
  3. Step 3: Cross multiply
    257,712x = 409,992 × 409,992
  4. Step 4: Simplify right side
    257,712x = 168,093,440,064
  5. Step 5: Solve for x
    x = 168,093,440,064/257,712
  6. Step 6: Final answer
    x = 652,253.06

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.