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Finding the Third Proportional to 256,208 and 409,294

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Solution

The third proportional to 256,208 and 409,294 is: 653,849.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    256,208 : 409,294 = 409,294 : x
  2. Step 2: Convert to fraction form
    256,208/409,294 = 409,294/x
  3. Step 3: Cross multiply
    256,208x = 409,294 × 409,294
  4. Step 4: Simplify right side
    256,208x = 167,521,578,436
  5. Step 5: Solve for x
    x = 167,521,578,436/256,208
  6. Step 6: Final answer
    x = 653,849.91

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Why These Related Problems?

These problems maintain the same ratio (1.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.