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Finding the Third Proportional to 10,214 and 14,385

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Solution

The third proportional to 10,214 and 14,385 is: 20,259.27

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,214 : 14,385 = 14,385 : x
  2. Step 2: Convert to fraction form
    10,214/14,385 = 14,385/x
  3. Step 3: Cross multiply
    10,214x = 14,385 × 14,385
  4. Step 4: Simplify right side
    10,214x = 206,928,225
  5. Step 5: Solve for x
    x = 206,928,225/10,214
  6. Step 6: Final answer
    x = 20,259.27

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.