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Finding the Third Proportional to 256,850 and 409,059

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Solution

The third proportional to 256,850 and 409,059 is: 651,466.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    256,850 : 409,059 = 409,059 : x
  2. Step 2: Convert to fraction form
    256,850/409,059 = 409,059/x
  3. Step 3: Cross multiply
    256,850x = 409,059 × 409,059
  4. Step 4: Simplify right side
    256,850x = 167,329,265,481
  5. Step 5: Solve for x
    x = 167,329,265,481/256,850
  6. Step 6: Final answer
    x = 651,466.87

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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.