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Finding the Third Proportional to 409,568 and 641,106

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Solution

The third proportional to 409,568 and 641,106 is: 1,003,537.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    409,568 : 641,106 = 641,106 : x
  2. Step 2: Convert to fraction form
    409,568/641,106 = 641,106/x
  3. Step 3: Cross multiply
    409,568x = 641,106 × 641,106
  4. Step 4: Simplify right side
    409,568x = 411,016,903,236
  5. Step 5: Solve for x
    x = 411,016,903,236/409,568
  6. Step 6: Final answer
    x = 1,003,537.64

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.