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Finding the Third Proportional to 519,781 and 777,514

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Solution

The third proportional to 519,781 and 777,514 is: 1,163,043.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    519,781 : 777,514 = 777,514 : x
  2. Step 2: Convert to fraction form
    519,781/777,514 = 777,514/x
  3. Step 3: Cross multiply
    519,781x = 777,514 × 777,514
  4. Step 4: Simplify right side
    519,781x = 604,528,020,196
  5. Step 5: Solve for x
    x = 604,528,020,196/519,781
  6. Step 6: Final answer
    x = 1,163,043.71

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.