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Finding the Third Proportional to 197,722 and 409,470

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Solution

The third proportional to 197,722 and 409,470 is: 847,986.98

Step by Step Solution

  1. Step 1: Write the proportion equation
    197,722 : 409,470 = 409,470 : x
  2. Step 2: Convert to fraction form
    197,722/409,470 = 409,470/x
  3. Step 3: Cross multiply
    197,722x = 409,470 × 409,470
  4. Step 4: Simplify right side
    197,722x = 167,665,680,900
  5. Step 5: Solve for x
    x = 167,665,680,900/197,722
  6. Step 6: Final answer
    x = 847,986.98

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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.