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Finding the Third Proportional to 97,677 and 200,538

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Solution

The third proportional to 97,677 and 200,538 is: 411,719.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    97,677 : 200,538 = 200,538 : x
  2. Step 2: Convert to fraction form
    97,677/200,538 = 200,538/x
  3. Step 3: Cross multiply
    97,677x = 200,538 × 200,538
  4. Step 4: Simplify right side
    97,677x = 40,215,489,444
  5. Step 5: Solve for x
    x = 40,215,489,444/97,677
  6. Step 6: Final answer
    x = 411,719.13

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.