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Finding the Third Proportional to 102.75 and 164.34

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Solution

The third proportional to 102.75 and 164.34 is: 262.86

Step by Step Solution

  1. Step 1: Write the proportion equation
    102.75 : 164.34 = 164.34 : x
  2. Step 2: Convert to fraction form
    102.75/164.34 = 164.34/x
  3. Step 3: Cross multiply
    102.75x = 164.34 × 164.34
  4. Step 4: Simplify right side
    102.75x = 27,008.87
  5. Step 5: Solve for x
    x = 27,008.87/102.75
  6. Step 6: Final answer
    x = 262.86

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Why These Related Problems?

These problems maintain the same ratio (1.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.