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Finding the Third Proportional to 415.13 and 442.34

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Solution

The third proportional to 415.13 and 442.34 is: 471.33

Step by Step Solution

  1. Step 1: Write the proportion equation
    415.13 : 442.34 = 442.34 : x
  2. Step 2: Convert to fraction form
    415.13/442.34 = 442.34/x
  3. Step 3: Cross multiply
    415.13x = 442.34 × 442.34
  4. Step 4: Simplify right side
    415.13x = 195,661.08
  5. Step 5: Solve for x
    x = 195,661.08/415.13
  6. Step 6: Final answer
    x = 471.33

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Why These Related Problems?

These problems maintain the same ratio (1.07) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.