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Finding the Third Proportional to 7,827 and 16,172

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Solution

The third proportional to 7,827 and 16,172 is: 33,414.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,827 : 16,172 = 16,172 : x
  2. Step 2: Convert to fraction form
    7,827/16,172 = 16,172/x
  3. Step 3: Cross multiply
    7,827x = 16,172 × 16,172
  4. Step 4: Simplify right side
    7,827x = 261,533,584
  5. Step 5: Solve for x
    x = 261,533,584/7,827
  6. Step 6: Final answer
    x = 33,414.28

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Why These Related Problems?

These problems maintain the same ratio (2.07) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.