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Finding the Third Proportional to 132,049 and 257,483

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Solution

The third proportional to 132,049 and 257,483 is: 502,067.38

Step by Step Solution

  1. Step 1: Write the proportion equation
    132,049 : 257,483 = 257,483 : x
  2. Step 2: Convert to fraction form
    132,049/257,483 = 257,483/x
  3. Step 3: Cross multiply
    132,049x = 257,483 × 257,483
  4. Step 4: Simplify right side
    132,049x = 66,297,495,289
  5. Step 5: Solve for x
    x = 66,297,495,289/132,049
  6. Step 6: Final answer
    x = 502,067.38

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Why These Related Problems?

These problems maintain the same ratio (1.95) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.