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Finding the Third Proportional to 10,821 and 23,207

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Solution

The third proportional to 10,821 and 23,207 is: 49,770.34

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,821 : 23,207 = 23,207 : x
  2. Step 2: Convert to fraction form
    10,821/23,207 = 23,207/x
  3. Step 3: Cross multiply
    10,821x = 23,207 × 23,207
  4. Step 4: Simplify right side
    10,821x = 538,564,849
  5. Step 5: Solve for x
    x = 538,564,849/10,821
  6. Step 6: Final answer
    x = 49,770.34

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.