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Finding the Third Proportional to 105,464 and 227,769

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Solution

The third proportional to 105,464 and 227,769 is: 491,909.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    105,464 : 227,769 = 227,769 : x
  2. Step 2: Convert to fraction form
    105,464/227,769 = 227,769/x
  3. Step 3: Cross multiply
    105,464x = 227,769 × 227,769
  4. Step 4: Simplify right side
    105,464x = 51,878,717,361
  5. Step 5: Solve for x
    x = 51,878,717,361/105,464
  6. Step 6: Final answer
    x = 491,909.25

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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.