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Finding the Third Proportional to 197,723 and 409,472

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Solution

The third proportional to 197,723 and 409,472 is: 847,990.97

Step by Step Solution

  1. Step 1: Write the proportion equation
    197,723 : 409,472 = 409,472 : x
  2. Step 2: Convert to fraction form
    197,723/409,472 = 409,472/x
  3. Step 3: Cross multiply
    197,723x = 409,472 × 409,472
  4. Step 4: Simplify right side
    197,723x = 167,667,318,784
  5. Step 5: Solve for x
    x = 167,667,318,784/197,723
  6. Step 6: Final answer
    x = 847,990.97

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Why These Related Problems?

These problems maintain the same ratio (2.07) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.