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Finding the Third Proportional to 102,024 and 209,206

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Solution

The third proportional to 102,024 and 209,206 is: 428,988.77

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,024 : 209,206 = 209,206 : x
  2. Step 2: Convert to fraction form
    102,024/209,206 = 209,206/x
  3. Step 3: Cross multiply
    102,024x = 209,206 × 209,206
  4. Step 4: Simplify right side
    102,024x = 43,767,150,436
  5. Step 5: Solve for x
    x = 43,767,150,436/102,024
  6. Step 6: Final answer
    x = 428,988.77

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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.