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Finding the Third Proportional to 384.47 and 414.84

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Solution

The third proportional to 384.47 and 414.84 is: 447.62

Step by Step Solution

  1. Step 1: Write the proportion equation
    384.47 : 414.84 = 414.84 : x
  2. Step 2: Convert to fraction form
    384.47/414.84 = 414.84/x
  3. Step 3: Cross multiply
    384.47x = 414.84 × 414.84
  4. Step 4: Simplify right side
    384.47x = 172,095.34
  5. Step 5: Solve for x
    x = 172,095.34/384.47
  6. Step 6: Final answer
    x = 447.62

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Why These Related Problems?

These problems maintain the same ratio (1.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.