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Finding the Third Proportional to 82,816 and 128,471

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Solution

The third proportional to 82,816 and 128,471 is: 199,294.80

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,816 : 128,471 = 128,471 : x
  2. Step 2: Convert to fraction form
    82,816/128,471 = 128,471/x
  3. Step 3: Cross multiply
    82,816x = 128,471 × 128,471
  4. Step 4: Simplify right side
    82,816x = 16,504,797,841
  5. Step 5: Solve for x
    x = 16,504,797,841/82,816
  6. Step 6: Final answer
    x = 199,294.80

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.