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Finding the Third Proportional to 273,681 and 409,419

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Solution

The third proportional to 273,681 and 409,419 is: 612,479.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    273,681 : 409,419 = 409,419 : x
  2. Step 2: Convert to fraction form
    273,681/409,419 = 409,419/x
  3. Step 3: Cross multiply
    273,681x = 409,419 × 409,419
  4. Step 4: Simplify right side
    273,681x = 167,623,917,561
  5. Step 5: Solve for x
    x = 167,623,917,561/273,681
  6. Step 6: Final answer
    x = 612,479.19

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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.