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Finding the Third Proportional to 321,854 and 685,288

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Solution

The third proportional to 321,854 and 685,288 is: 1,459,107.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    321,854 : 685,288 = 685,288 : x
  2. Step 2: Convert to fraction form
    321,854/685,288 = 685,288/x
  3. Step 3: Cross multiply
    321,854x = 685,288 × 685,288
  4. Step 4: Simplify right side
    321,854x = 469,619,642,944
  5. Step 5: Solve for x
    x = 469,619,642,944/321,854
  6. Step 6: Final answer
    x = 1,459,107.68

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.