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Finding the Third Proportional to 10,583 and 16,214

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Solution

The third proportional to 10,583 and 16,214 is: 24,841.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,583 : 16,214 = 16,214 : x
  2. Step 2: Convert to fraction form
    10,583/16,214 = 16,214/x
  3. Step 3: Cross multiply
    10,583x = 16,214 × 16,214
  4. Step 4: Simplify right side
    10,583x = 262,893,796
  5. Step 5: Solve for x
    x = 262,893,796/10,583
  6. Step 6: Final answer
    x = 24,841.14

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Why These Related Problems?

These problems maintain the same ratio (1.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.