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Finding the Third Proportional to 409.92 and 582.75

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Solution

The third proportional to 409.92 and 582.75 is: 828.44

Step by Step Solution

  1. Step 1: Write the proportion equation
    409.92 : 582.75 = 582.75 : x
  2. Step 2: Convert to fraction form
    409.92/582.75 = 582.75/x
  3. Step 3: Cross multiply
    409.92x = 582.75 × 582.75
  4. Step 4: Simplify right side
    409.92x = 339,597.56
  5. Step 5: Solve for x
    x = 339,597.56/409.92
  6. Step 6: Final answer
    x = 828.44

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.