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Finding the Third Proportional to 462,069 and 578,406

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Solution

The third proportional to 462,069 and 578,406 is: 724,033.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    462,069 : 578,406 = 578,406 : x
  2. Step 2: Convert to fraction form
    462,069/578,406 = 578,406/x
  3. Step 3: Cross multiply
    462,069x = 578,406 × 578,406
  4. Step 4: Simplify right side
    462,069x = 334,553,500,836
  5. Step 5: Solve for x
    x = 334,553,500,836/462,069
  6. Step 6: Final answer
    x = 724,033.64

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Why These Related Problems?

These problems maintain the same ratio (1.25) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.