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Finding the Third Proportional to 96,384 and 199,471

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Solution

The third proportional to 96,384 and 199,471 is: 412,814.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    96,384 : 199,471 = 199,471 : x
  2. Step 2: Convert to fraction form
    96,384/199,471 = 199,471/x
  3. Step 3: Cross multiply
    96,384x = 199,471 × 199,471
  4. Step 4: Simplify right side
    96,384x = 39,788,679,841
  5. Step 5: Solve for x
    x = 39,788,679,841/96,384
  6. Step 6: Final answer
    x = 412,814.16

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Why These Related Problems?

These problems maintain the same ratio (2.07) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.