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Finding the Third Proportional to 99,021 and 213,824

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Solution

The third proportional to 99,021 and 213,824 is: 461,727.34

Step by Step Solution

  1. Step 1: Write the proportion equation
    99,021 : 213,824 = 213,824 : x
  2. Step 2: Convert to fraction form
    99,021/213,824 = 213,824/x
  3. Step 3: Cross multiply
    99,021x = 213,824 × 213,824
  4. Step 4: Simplify right side
    99,021x = 45,720,702,976
  5. Step 5: Solve for x
    x = 45,720,702,976/99,021
  6. Step 6: Final answer
    x = 461,727.34

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.