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Finding the Third Proportional to 678,108 and 829,740

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Solution

The third proportional to 678,108 and 829,740 is: 1,015,278.49

Step by Step Solution

  1. Step 1: Write the proportion equation
    678,108 : 829,740 = 829,740 : x
  2. Step 2: Convert to fraction form
    678,108/829,740 = 829,740/x
  3. Step 3: Cross multiply
    678,108x = 829,740 × 829,740
  4. Step 4: Simplify right side
    678,108x = 688,468,467,600
  5. Step 5: Solve for x
    x = 688,468,467,600/678,108
  6. Step 6: Final answer
    x = 1,015,278.49

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Why These Related Problems?

These problems maintain the same ratio (1.22) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.