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Finding the Third Proportional to 256,284 and 408,114

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Solution

The third proportional to 256,284 and 408,114 is: 649,892.45

Step by Step Solution

  1. Step 1: Write the proportion equation
    256,284 : 408,114 = 408,114 : x
  2. Step 2: Convert to fraction form
    256,284/408,114 = 408,114/x
  3. Step 3: Cross multiply
    256,284x = 408,114 × 408,114
  4. Step 4: Simplify right side
    256,284x = 166,557,036,996
  5. Step 5: Solve for x
    x = 166,557,036,996/256,284
  6. Step 6: Final answer
    x = 649,892.45

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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.