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Finding the Third Proportional to 258,786 and 411,507

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Solution

The third proportional to 258,786 and 411,507 is: 654,355.38

Step by Step Solution

  1. Step 1: Write the proportion equation
    258,786 : 411,507 = 411,507 : x
  2. Step 2: Convert to fraction form
    258,786/411,507 = 411,507/x
  3. Step 3: Cross multiply
    258,786x = 411,507 × 411,507
  4. Step 4: Simplify right side
    258,786x = 169,338,011,049
  5. Step 5: Solve for x
    x = 169,338,011,049/258,786
  6. Step 6: Final answer
    x = 654,355.38

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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.