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Finding the Third Proportional to 7,834 and 16,214

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Solution

The third proportional to 7,834 and 16,214 is: 33,558.05

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,834 : 16,214 = 16,214 : x
  2. Step 2: Convert to fraction form
    7,834/16,214 = 16,214/x
  3. Step 3: Cross multiply
    7,834x = 16,214 × 16,214
  4. Step 4: Simplify right side
    7,834x = 262,893,796
  5. Step 5: Solve for x
    x = 262,893,796/7,834
  6. Step 6: Final answer
    x = 33,558.05

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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.