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Finding the Third Proportional to 197,724 and 409,474

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Solution

The third proportional to 197,724 and 409,474 is: 847,994.97

Step by Step Solution

  1. Step 1: Write the proportion equation
    197,724 : 409,474 = 409,474 : x
  2. Step 2: Convert to fraction form
    197,724/409,474 = 409,474/x
  3. Step 3: Cross multiply
    197,724x = 409,474 × 409,474
  4. Step 4: Simplify right side
    197,724x = 167,668,956,676
  5. Step 5: Solve for x
    x = 167,668,956,676/197,724
  6. Step 6: Final answer
    x = 847,994.97

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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.