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Finding the Third Proportional to 102,546 and 213,258

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Solution

The third proportional to 102,546 and 213,258 is: 443,498.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,546 : 213,258 = 213,258 : x
  2. Step 2: Convert to fraction form
    102,546/213,258 = 213,258/x
  3. Step 3: Cross multiply
    102,546x = 213,258 × 213,258
  4. Step 4: Simplify right side
    102,546x = 45,478,974,564
  5. Step 5: Solve for x
    x = 45,478,974,564/102,546
  6. Step 6: Final answer
    x = 443,498.28

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Why These Related Problems?

These problems maintain the same ratio (2.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.