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Finding the Third Proportional to 257,524 and 413,646

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Solution

The third proportional to 257,524 and 413,646 is: 664,415.80

Step by Step Solution

  1. Step 1: Write the proportion equation
    257,524 : 413,646 = 413,646 : x
  2. Step 2: Convert to fraction form
    257,524/413,646 = 413,646/x
  3. Step 3: Cross multiply
    257,524x = 413,646 × 413,646
  4. Step 4: Simplify right side
    257,524x = 171,103,013,316
  5. Step 5: Solve for x
    x = 171,103,013,316/257,524
  6. Step 6: Final answer
    x = 664,415.80

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Why These Related Problems?

These problems maintain the same ratio (1.61) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.