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Finding the Third Proportional to 257,936 and 398,412

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Solution

The third proportional to 257,936 and 398,412 is: 615,393.44

Step by Step Solution

  1. Step 1: Write the proportion equation
    257,936 : 398,412 = 398,412 : x
  2. Step 2: Convert to fraction form
    257,936/398,412 = 398,412/x
  3. Step 3: Cross multiply
    257,936x = 398,412 × 398,412
  4. Step 4: Simplify right side
    257,936x = 158,732,121,744
  5. Step 5: Solve for x
    x = 158,732,121,744/257,936
  6. Step 6: Final answer
    x = 615,393.44

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.