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Finding the Third Proportional to 4,091 and 9,728

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Solution

The third proportional to 4,091 and 9,728 is: 23,132.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,091 : 9,728 = 9,728 : x
  2. Step 2: Convert to fraction form
    4,091/9,728 = 9,728/x
  3. Step 3: Cross multiply
    4,091x = 9,728 × 9,728
  4. Step 4: Simplify right side
    4,091x = 94,633,984
  5. Step 5: Solve for x
    x = 94,633,984/4,091
  6. Step 6: Final answer
    x = 23,132.24

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Why These Related Problems?

These problems maintain the same ratio (2.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.