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Finding the Third Proportional to 102,021 and 216,165

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Solution

The third proportional to 102,021 and 216,165 is: 458,016.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,021 : 216,165 = 216,165 : x
  2. Step 2: Convert to fraction form
    102,021/216,165 = 216,165/x
  3. Step 3: Cross multiply
    102,021x = 216,165 × 216,165
  4. Step 4: Simplify right side
    102,021x = 46,727,307,225
  5. Step 5: Solve for x
    x = 46,727,307,225/102,021
  6. Step 6: Final answer
    x = 458,016.56

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Why These Related Problems?

These problems maintain the same ratio (2.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.