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Finding the Third Proportional to 321,569 and 685,854

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Solution

The third proportional to 321,569 and 685,854 is: 1,462,814.23

Step by Step Solution

  1. Step 1: Write the proportion equation
    321,569 : 685,854 = 685,854 : x
  2. Step 2: Convert to fraction form
    321,569/685,854 = 685,854/x
  3. Step 3: Cross multiply
    321,569x = 685,854 × 685,854
  4. Step 4: Simplify right side
    321,569x = 470,395,709,316
  5. Step 5: Solve for x
    x = 470,395,709,316/321,569
  6. Step 6: Final answer
    x = 1,462,814.23

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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.