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Finding the Third Proportional to 198,322 and 407,202

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Solution

The third proportional to 198,322 and 407,202 is: 836,082.07

Step by Step Solution

  1. Step 1: Write the proportion equation
    198,322 : 407,202 = 407,202 : x
  2. Step 2: Convert to fraction form
    198,322/407,202 = 407,202/x
  3. Step 3: Cross multiply
    198,322x = 407,202 × 407,202
  4. Step 4: Simplify right side
    198,322x = 165,813,468,804
  5. Step 5: Solve for x
    x = 165,813,468,804/198,322
  6. Step 6: Final answer
    x = 836,082.07

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.