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Finding the Third Proportional to 8,178 and 9,834

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Solution

The third proportional to 8,178 and 9,834 is: 11,825.33

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,178 : 9,834 = 9,834 : x
  2. Step 2: Convert to fraction form
    8,178/9,834 = 9,834/x
  3. Step 3: Cross multiply
    8,178x = 9,834 × 9,834
  4. Step 4: Simplify right side
    8,178x = 96,707,556
  5. Step 5: Solve for x
    x = 96,707,556/8,178
  6. Step 6: Final answer
    x = 11,825.33

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Why These Related Problems?

These problems maintain the same ratio (1.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.