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Finding the Third Proportional to 209,786 and 322,643

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Solution

The third proportional to 209,786 and 322,643 is: 496,212.83

Step by Step Solution

  1. Step 1: Write the proportion equation
    209,786 : 322,643 = 322,643 : x
  2. Step 2: Convert to fraction form
    209,786/322,643 = 322,643/x
  3. Step 3: Cross multiply
    209,786x = 322,643 × 322,643
  4. Step 4: Simplify right side
    209,786x = 104,098,505,449
  5. Step 5: Solve for x
    x = 104,098,505,449/209,786
  6. Step 6: Final answer
    x = 496,212.83

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.