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Finding the Third Proportional to 37,681 and 81,842

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Solution

The third proportional to 37,681 and 81,842 is: 177,758.37

Step by Step Solution

  1. Step 1: Write the proportion equation
    37,681 : 81,842 = 81,842 : x
  2. Step 2: Convert to fraction form
    37,681/81,842 = 81,842/x
  3. Step 3: Cross multiply
    37,681x = 81,842 × 81,842
  4. Step 4: Simplify right side
    37,681x = 6,698,112,964
  5. Step 5: Solve for x
    x = 6,698,112,964/37,681
  6. Step 6: Final answer
    x = 177,758.37

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.