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Finding the Third Proportional to 197,722 and 411,828

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Solution

The third proportional to 197,722 and 411,828 is: 857,781.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    197,722 : 411,828 = 411,828 : x
  2. Step 2: Convert to fraction form
    197,722/411,828 = 411,828/x
  3. Step 3: Cross multiply
    197,722x = 411,828 × 411,828
  4. Step 4: Simplify right side
    197,722x = 169,602,301,584
  5. Step 5: Solve for x
    x = 169,602,301,584/197,722
  6. Step 6: Final answer
    x = 857,781.64

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Why These Related Problems?

These problems maintain the same ratio (2.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.