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Finding the Third Proportional to 8,192 and 9,032

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Solution

The third proportional to 8,192 and 9,032 is: 9,958.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,192 : 9,032 = 9,032 : x
  2. Step 2: Convert to fraction form
    8,192/9,032 = 9,032/x
  3. Step 3: Cross multiply
    8,192x = 9,032 × 9,032
  4. Step 4: Simplify right side
    8,192x = 81,577,024
  5. Step 5: Solve for x
    x = 81,577,024/8,192
  6. Step 6: Final answer
    x = 9,958.13

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.