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Finding the Third Proportional to 205,509 and 322,466

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Solution

The third proportional to 205,509 and 322,466 is: 505,984.27

Step by Step Solution

  1. Step 1: Write the proportion equation
    205,509 : 322,466 = 322,466 : x
  2. Step 2: Convert to fraction form
    205,509/322,466 = 322,466/x
  3. Step 3: Cross multiply
    205,509x = 322,466 × 322,466
  4. Step 4: Simplify right side
    205,509x = 103,984,321,156
  5. Step 5: Solve for x
    x = 103,984,321,156/205,509
  6. Step 6: Final answer
    x = 505,984.27

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.