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Finding the Third Proportional to 382,102 and 830,542

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Solution

The third proportional to 382,102 and 830,542 is: 1,805,277.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    382,102 : 830,542 = 830,542 : x
  2. Step 2: Convert to fraction form
    382,102/830,542 = 830,542/x
  3. Step 3: Cross multiply
    382,102x = 830,542 × 830,542
  4. Step 4: Simplify right side
    382,102x = 689,800,013,764
  5. Step 5: Solve for x
    x = 689,800,013,764/382,102
  6. Step 6: Final answer
    x = 1,805,277.16

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.