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Finding the Third Proportional to 10,522 and 14,497

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Solution

The third proportional to 10,522 and 14,497 is: 19,973.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,522 : 14,497 = 14,497 : x
  2. Step 2: Convert to fraction form
    10,522/14,497 = 14,497/x
  3. Step 3: Cross multiply
    10,522x = 14,497 × 14,497
  4. Step 4: Simplify right side
    10,522x = 210,163,009
  5. Step 5: Solve for x
    x = 210,163,009/10,522
  6. Step 6: Final answer
    x = 19,973.68

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.