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Finding the Third Proportional to 102,072 and 218,901

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Solution

The third proportional to 102,072 and 218,901 is: 469,449.48

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,072 : 218,901 = 218,901 : x
  2. Step 2: Convert to fraction form
    102,072/218,901 = 218,901/x
  3. Step 3: Cross multiply
    102,072x = 218,901 × 218,901
  4. Step 4: Simplify right side
    102,072x = 47,917,647,801
  5. Step 5: Solve for x
    x = 47,917,647,801/102,072
  6. Step 6: Final answer
    x = 469,449.48

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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.