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Finding the Third Proportional to 256,892 and 409,120

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Solution

The third proportional to 256,892 and 409,120 is: 651,554.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    256,892 : 409,120 = 409,120 : x
  2. Step 2: Convert to fraction form
    256,892/409,120 = 409,120/x
  3. Step 3: Cross multiply
    256,892x = 409,120 × 409,120
  4. Step 4: Simplify right side
    256,892x = 167,379,174,400
  5. Step 5: Solve for x
    x = 167,379,174,400/256,892
  6. Step 6: Final answer
    x = 651,554.64

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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.