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Finding the Third Proportional to 198,049 and 412,417

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Solution

The third proportional to 198,049 and 412,417 is: 858,816.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    198,049 : 412,417 = 412,417 : x
  2. Step 2: Convert to fraction form
    198,049/412,417 = 412,417/x
  3. Step 3: Cross multiply
    198,049x = 412,417 × 412,417
  4. Step 4: Simplify right side
    198,049x = 170,087,781,889
  5. Step 5: Solve for x
    x = 170,087,781,889/198,049
  6. Step 6: Final answer
    x = 858,816.67

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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.