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Finding the Third Proportional to 4,096 and 9,584

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Solution

The third proportional to 4,096 and 9,584 is: 22,425.06

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,096 : 9,584 = 9,584 : x
  2. Step 2: Convert to fraction form
    4,096/9,584 = 9,584/x
  3. Step 3: Cross multiply
    4,096x = 9,584 × 9,584
  4. Step 4: Simplify right side
    4,096x = 91,853,056
  5. Step 5: Solve for x
    x = 91,853,056/4,096
  6. Step 6: Final answer
    x = 22,425.06

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Why These Related Problems?

These problems maintain the same ratio (2.34) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.