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Finding the Third Proportional to 17,784 and 38,031

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Solution

The third proportional to 17,784 and 38,031 is: 81,329.11

Step by Step Solution

  1. Step 1: Write the proportion equation
    17,784 : 38,031 = 38,031 : x
  2. Step 2: Convert to fraction form
    17,784/38,031 = 38,031/x
  3. Step 3: Cross multiply
    17,784x = 38,031 × 38,031
  4. Step 4: Simplify right side
    17,784x = 1,446,356,961
  5. Step 5: Solve for x
    x = 1,446,356,961/17,784
  6. Step 6: Final answer
    x = 81,329.11

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.