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Finding the Third Proportional to 8,509 and 13,057

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Solution

The third proportional to 8,509 and 13,057 is: 20,035.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,509 : 13,057 = 13,057 : x
  2. Step 2: Convert to fraction form
    8,509/13,057 = 13,057/x
  3. Step 3: Cross multiply
    8,509x = 13,057 × 13,057
  4. Step 4: Simplify right side
    8,509x = 170,485,249
  5. Step 5: Solve for x
    x = 170,485,249/8,509
  6. Step 6: Final answer
    x = 20,035.87

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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.