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Finding the Third Proportional to 381,410 and 829,228

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Solution

The third proportional to 381,410 and 829,228 is: 1,802,834.42

Step by Step Solution

  1. Step 1: Write the proportion equation
    381,410 : 829,228 = 829,228 : x
  2. Step 2: Convert to fraction form
    381,410/829,228 = 829,228/x
  3. Step 3: Cross multiply
    381,410x = 829,228 × 829,228
  4. Step 4: Simplify right side
    381,410x = 687,619,075,984
  5. Step 5: Solve for x
    x = 687,619,075,984/381,410
  6. Step 6: Final answer
    x = 1,802,834.42

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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.