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Finding the Third Proportional to 263,800 and 409,086

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Solution

The third proportional to 263,800 and 409,086 is: 634,387.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    263,800 : 409,086 = 409,086 : x
  2. Step 2: Convert to fraction form
    263,800/409,086 = 409,086/x
  3. Step 3: Cross multiply
    263,800x = 409,086 × 409,086
  4. Step 4: Simplify right side
    263,800x = 167,351,355,396
  5. Step 5: Solve for x
    x = 167,351,355,396/263,800
  6. Step 6: Final answer
    x = 634,387.25

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.