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Finding the Third Proportional to 6,800 and 16,382

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Solution

The third proportional to 6,800 and 16,382 is: 39,466.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,800 : 16,382 = 16,382 : x
  2. Step 2: Convert to fraction form
    6,800/16,382 = 16,382/x
  3. Step 3: Cross multiply
    6,800x = 16,382 × 16,382
  4. Step 4: Simplify right side
    6,800x = 268,369,924
  5. Step 5: Solve for x
    x = 268,369,924/6,800
  6. Step 6: Final answer
    x = 39,466.17

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Why These Related Problems?

These problems maintain the same ratio (2.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.