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Finding the Third Proportional to 415.97 and 442.69

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Solution

The third proportional to 415.97 and 442.69 is: 471.12

Step by Step Solution

  1. Step 1: Write the proportion equation
    415.97 : 442.69 = 442.69 : x
  2. Step 2: Convert to fraction form
    415.97/442.69 = 442.69/x
  3. Step 3: Cross multiply
    415.97x = 442.69 × 442.69
  4. Step 4: Simplify right side
    415.97x = 195,972.22
  5. Step 5: Solve for x
    x = 195,972.22/415.97
  6. Step 6: Final answer
    x = 471.12

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Why These Related Problems?

These problems maintain the same ratio (1.06) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.