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Finding the Third Proportional to 198.07 and 415.76

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Solution

The third proportional to 198.07 and 415.76 is: 872.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    198.07 : 415.76 = 415.76 : x
  2. Step 2: Convert to fraction form
    198.07/415.76 = 415.76/x
  3. Step 3: Cross multiply
    198.07x = 415.76 × 415.76
  4. Step 4: Simplify right side
    198.07x = 172,854.56
  5. Step 5: Solve for x
    x = 172,854.56/198.07
  6. Step 6: Final answer
    x = 872.69

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Why These Related Problems?

These problems maintain the same ratio (2.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.