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Finding the Third Proportional to 213,012 and 323,406

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Solution

The third proportional to 213,012 and 323,406 is: 491,011.97

Step by Step Solution

  1. Step 1: Write the proportion equation
    213,012 : 323,406 = 323,406 : x
  2. Step 2: Convert to fraction form
    213,012/323,406 = 323,406/x
  3. Step 3: Cross multiply
    213,012x = 323,406 × 323,406
  4. Step 4: Simplify right side
    213,012x = 104,591,440,836
  5. Step 5: Solve for x
    x = 104,591,440,836/213,012
  6. Step 6: Final answer
    x = 491,011.97

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Why These Related Problems?

These problems maintain the same ratio (1.52) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.