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Finding the Third Proportional to 405 and 822.38

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Solution

The third proportional to 405 and 822.38 is: 1,669.88

Step by Step Solution

  1. Step 1: Write the proportion equation
    405 : 822.38 = 822.38 : x
  2. Step 2: Convert to fraction form
    405/822.38 = 822.38/x
  3. Step 3: Cross multiply
    405x = 822.38 × 822.38
  4. Step 4: Simplify right side
    405x = 676,300.64
  5. Step 5: Solve for x
    x = 676,300.64/405
  6. Step 6: Final answer
    x = 1,669.88

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Why These Related Problems?

These problems maintain the same ratio (2.03) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.