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Finding the Third Proportional to 102.09 and 194.06

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Solution

The third proportional to 102.09 and 194.06 is: 368.88

Step by Step Solution

  1. Step 1: Write the proportion equation
    102.09 : 194.06 = 194.06 : x
  2. Step 2: Convert to fraction form
    102.09/194.06 = 194.06/x
  3. Step 3: Cross multiply
    102.09x = 194.06 × 194.06
  4. Step 4: Simplify right side
    102.09x = 37,660.25
  5. Step 5: Solve for x
    x = 37,660.25/102.09
  6. Step 6: Final answer
    x = 368.88

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Why These Related Problems?

These problems maintain the same ratio (1.90) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.