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Finding the Third Proportional to 257,198 and 409,269

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Solution

The third proportional to 257,198 and 409,269 is: 651,253.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    257,198 : 409,269 = 409,269 : x
  2. Step 2: Convert to fraction form
    257,198/409,269 = 409,269/x
  3. Step 3: Cross multiply
    257,198x = 409,269 × 409,269
  4. Step 4: Simplify right side
    257,198x = 167,501,114,361
  5. Step 5: Solve for x
    x = 167,501,114,361/257,198
  6. Step 6: Final answer
    x = 651,253.56

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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.