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Finding the Third Proportional to 407,876 and 827,140

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Solution

The third proportional to 407,876 and 827,140 is: 1,677,373.96

Step by Step Solution

  1. Step 1: Write the proportion equation
    407,876 : 827,140 = 827,140 : x
  2. Step 2: Convert to fraction form
    407,876/827,140 = 827,140/x
  3. Step 3: Cross multiply
    407,876x = 827,140 × 827,140
  4. Step 4: Simplify right side
    407,876x = 684,160,579,600
  5. Step 5: Solve for x
    x = 684,160,579,600/407,876
  6. Step 6: Final answer
    x = 1,677,373.96

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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.