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Finding the Third Proportional to 257,514 and 397,944

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Solution

The third proportional to 257,514 and 397,944 is: 614,954.63

Step by Step Solution

  1. Step 1: Write the proportion equation
    257,514 : 397,944 = 397,944 : x
  2. Step 2: Convert to fraction form
    257,514/397,944 = 397,944/x
  3. Step 3: Cross multiply
    257,514x = 397,944 × 397,944
  4. Step 4: Simplify right side
    257,514x = 158,359,427,136
  5. Step 5: Solve for x
    x = 158,359,427,136/257,514
  6. Step 6: Final answer
    x = 614,954.63

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.