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Finding the Third Proportional to 198,051 and 412,421

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Solution

The third proportional to 198,051 and 412,421 is: 858,824.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    198,051 : 412,421 = 412,421 : x
  2. Step 2: Convert to fraction form
    198,051/412,421 = 412,421/x
  3. Step 3: Cross multiply
    198,051x = 412,421 × 412,421
  4. Step 4: Simplify right side
    198,051x = 170,091,081,241
  5. Step 5: Solve for x
    x = 170,091,081,241/198,051
  6. Step 6: Final answer
    x = 858,824.65

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Why These Related Problems?

These problems maintain the same ratio (2.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.