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Finding the Third Proportional to 4,100 and 9,686

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Solution

The third proportional to 4,100 and 9,686 is: 22,882.58

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,100 : 9,686 = 9,686 : x
  2. Step 2: Convert to fraction form
    4,100/9,686 = 9,686/x
  3. Step 3: Cross multiply
    4,100x = 9,686 × 9,686
  4. Step 4: Simplify right side
    4,100x = 93,818,596
  5. Step 5: Solve for x
    x = 93,818,596/4,100
  6. Step 6: Final answer
    x = 22,882.58

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Why These Related Problems?

These problems maintain the same ratio (2.36) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.