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Finding the Third Proportional to 77,814 and 165,996

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Solution

The third proportional to 77,814 and 165,996 is: 354,109.44

Step by Step Solution

  1. Step 1: Write the proportion equation
    77,814 : 165,996 = 165,996 : x
  2. Step 2: Convert to fraction form
    77,814/165,996 = 165,996/x
  3. Step 3: Cross multiply
    77,814x = 165,996 × 165,996
  4. Step 4: Simplify right side
    77,814x = 27,554,672,016
  5. Step 5: Solve for x
    x = 27,554,672,016/77,814
  6. Step 6: Final answer
    x = 354,109.44

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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.