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Finding the Third Proportional to 527,414 and 781,257

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Solution

The third proportional to 527,414 and 781,257 is: 1,157,273.98

Step by Step Solution

  1. Step 1: Write the proportion equation
    527,414 : 781,257 = 781,257 : x
  2. Step 2: Convert to fraction form
    527,414/781,257 = 781,257/x
  3. Step 3: Cross multiply
    527,414x = 781,257 × 781,257
  4. Step 4: Simplify right side
    527,414x = 610,362,500,049
  5. Step 5: Solve for x
    x = 610,362,500,049/527,414
  6. Step 6: Final answer
    x = 1,157,273.98

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Why These Related Problems?

These problems maintain the same ratio (1.48) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.