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Finding the Third Proportional to 407,858 and 827,106

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Solution

The third proportional to 407,858 and 827,106 is: 1,677,310.08

Step by Step Solution

  1. Step 1: Write the proportion equation
    407,858 : 827,106 = 827,106 : x
  2. Step 2: Convert to fraction form
    407,858/827,106 = 827,106/x
  3. Step 3: Cross multiply
    407,858x = 827,106 × 827,106
  4. Step 4: Simplify right side
    407,858x = 684,104,335,236
  5. Step 5: Solve for x
    x = 684,104,335,236/407,858
  6. Step 6: Final answer
    x = 1,677,310.08

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Why These Related Problems?

These problems maintain the same ratio (2.03) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.