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Finding the Third Proportional to 512,272 and 823,083

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Solution

The third proportional to 512,272 and 823,083 is: 1,322,472.49

Step by Step Solution

  1. Step 1: Write the proportion equation
    512,272 : 823,083 = 823,083 : x
  2. Step 2: Convert to fraction form
    512,272/823,083 = 823,083/x
  3. Step 3: Cross multiply
    512,272x = 823,083 × 823,083
  4. Step 4: Simplify right side
    512,272x = 677,465,624,889
  5. Step 5: Solve for x
    x = 677,465,624,889/512,272
  6. Step 6: Final answer
    x = 1,322,472.49

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Why These Related Problems?

These problems maintain the same ratio (1.61) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.