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Finding the Third Proportional to 81,942 and 177,004

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Solution

The third proportional to 81,942 and 177,004 is: 382,348.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    81,942 : 177,004 = 177,004 : x
  2. Step 2: Convert to fraction form
    81,942/177,004 = 177,004/x
  3. Step 3: Cross multiply
    81,942x = 177,004 × 177,004
  4. Step 4: Simplify right side
    81,942x = 31,330,416,016
  5. Step 5: Solve for x
    x = 31,330,416,016/81,942
  6. Step 6: Final answer
    x = 382,348.69

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.