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Finding the Third Proportional to 381,314 and 829,026

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Solution

The third proportional to 381,314 and 829,026 is: 1,802,409.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    381,314 : 829,026 = 829,026 : x
  2. Step 2: Convert to fraction form
    381,314/829,026 = 829,026/x
  3. Step 3: Cross multiply
    381,314x = 829,026 × 829,026
  4. Step 4: Simplify right side
    381,314x = 687,284,108,676
  5. Step 5: Solve for x
    x = 687,284,108,676/381,314
  6. Step 6: Final answer
    x = 1,802,409.85

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.