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Finding the Third Proportional to 97,769 and 213,217

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Solution

The third proportional to 97,769 and 213,217 is: 464,988.79

Step by Step Solution

  1. Step 1: Write the proportion equation
    97,769 : 213,217 = 213,217 : x
  2. Step 2: Convert to fraction form
    97,769/213,217 = 213,217/x
  3. Step 3: Cross multiply
    97,769x = 213,217 × 213,217
  4. Step 4: Simplify right side
    97,769x = 45,461,489,089
  5. Step 5: Solve for x
    x = 45,461,489,089/97,769
  6. Step 6: Final answer
    x = 464,988.79

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.