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Finding the Third Proportional to 205,442 and 288,459

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Solution

The third proportional to 205,442 and 288,459 is: 405,022.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    205,442 : 288,459 = 288,459 : x
  2. Step 2: Convert to fraction form
    205,442/288,459 = 288,459/x
  3. Step 3: Cross multiply
    205,442x = 288,459 × 288,459
  4. Step 4: Simplify right side
    205,442x = 83,208,594,681
  5. Step 5: Solve for x
    x = 83,208,594,681/205,442
  6. Step 6: Final answer
    x = 405,022.32

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Why These Related Problems?

These problems maintain the same ratio (1.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.