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Finding the Third Proportional to 77,096 and 164,032

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Solution

The third proportional to 77,096 and 164,032 is: 348,999.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    77,096 : 164,032 = 164,032 : x
  2. Step 2: Convert to fraction form
    77,096/164,032 = 164,032/x
  3. Step 3: Cross multiply
    77,096x = 164,032 × 164,032
  4. Step 4: Simplify right side
    77,096x = 26,906,497,024
  5. Step 5: Solve for x
    x = 26,906,497,024/77,096
  6. Step 6: Final answer
    x = 348,999.91

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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.