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Finding the Third Proportional to 9,786 and 22,533

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Solution

The third proportional to 9,786 and 22,533 is: 51,883.92

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,786 : 22,533 = 22,533 : x
  2. Step 2: Convert to fraction form
    9,786/22,533 = 22,533/x
  3. Step 3: Cross multiply
    9,786x = 22,533 × 22,533
  4. Step 4: Simplify right side
    9,786x = 507,736,089
  5. Step 5: Solve for x
    x = 507,736,089/9,786
  6. Step 6: Final answer
    x = 51,883.92

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Why These Related Problems?

These problems maintain the same ratio (2.30) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.