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Finding the Third Proportional to 381.66 and 822.09

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Solution

The third proportional to 381.66 and 822.09 is: 1,770.80

Step by Step Solution

  1. Step 1: Write the proportion equation
    381.66 : 822.09 = 822.09 : x
  2. Step 2: Convert to fraction form
    381.66/822.09 = 822.09/x
  3. Step 3: Cross multiply
    381.66x = 822.09 × 822.09
  4. Step 4: Simplify right side
    381.66x = 675,838.13
  5. Step 5: Solve for x
    x = 675,838.13/381.66
  6. Step 6: Final answer
    x = 1,770.80

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.