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Finding the Third Proportional to 199,007 and 409,694

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Solution

The third proportional to 199,007 and 409,694 is: 843,433.52

Step by Step Solution

  1. Step 1: Write the proportion equation
    199,007 : 409,694 = 409,694 : x
  2. Step 2: Convert to fraction form
    199,007/409,694 = 409,694/x
  3. Step 3: Cross multiply
    199,007x = 409,694 × 409,694
  4. Step 4: Simplify right side
    199,007x = 167,849,173,636
  5. Step 5: Solve for x
    x = 167,849,173,636/199,007
  6. Step 6: Final answer
    x = 843,433.52

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Why These Related Problems?

These problems maintain the same ratio (2.06) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.