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Finding the Third Proportional to 9,840 and 20,138

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Solution

The third proportional to 9,840 and 20,138 is: 41,213.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,840 : 20,138 = 20,138 : x
  2. Step 2: Convert to fraction form
    9,840/20,138 = 20,138/x
  3. Step 3: Cross multiply
    9,840x = 20,138 × 20,138
  4. Step 4: Simplify right side
    9,840x = 405,539,044
  5. Step 5: Solve for x
    x = 405,539,044/9,840
  6. Step 6: Final answer
    x = 41,213.32

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.