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Finding the Third Proportional to 97,684 and 208,016

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Solution

The third proportional to 97,684 and 208,016 is: 442,965.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    97,684 : 208,016 = 208,016 : x
  2. Step 2: Convert to fraction form
    97,684/208,016 = 208,016/x
  3. Step 3: Cross multiply
    97,684x = 208,016 × 208,016
  4. Step 4: Simplify right side
    97,684x = 43,270,656,256
  5. Step 5: Solve for x
    x = 43,270,656,256/97,684
  6. Step 6: Final answer
    x = 442,965.65

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.