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Finding the Third Proportional to 9,830 and 23,757

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Solution

The third proportional to 9,830 and 23,757 is: 57,415.57

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,830 : 23,757 = 23,757 : x
  2. Step 2: Convert to fraction form
    9,830/23,757 = 23,757/x
  3. Step 3: Cross multiply
    9,830x = 23,757 × 23,757
  4. Step 4: Simplify right side
    9,830x = 564,395,049
  5. Step 5: Solve for x
    x = 564,395,049/9,830
  6. Step 6: Final answer
    x = 57,415.57

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Why These Related Problems?

These problems maintain the same ratio (2.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.