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Finding the Third Proportional to 19,683 and 40,338

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Solution

The third proportional to 19,683 and 40,338 is: 82,668

Step by Step Solution

  1. Step 1: Write the proportion equation
    19,683 : 40,338 = 40,338 : x
  2. Step 2: Convert to fraction form
    19,683/40,338 = 40,338/x
  3. Step 3: Cross multiply
    19,683x = 40,338 × 40,338
  4. Step 4: Simplify right side
    19,683x = 1,627,154,244
  5. Step 5: Solve for x
    x = 1,627,154,244/19,683
  6. Step 6: Final answer
    x = 82,668

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.