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Finding the Third Proportional to 289,919 and 461,231

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Solution

The third proportional to 289,919 and 461,231 is: 733,770.59

Step by Step Solution

  1. Step 1: Write the proportion equation
    289,919 : 461,231 = 461,231 : x
  2. Step 2: Convert to fraction form
    289,919/461,231 = 461,231/x
  3. Step 3: Cross multiply
    289,919x = 461,231 × 461,231
  4. Step 4: Simplify right side
    289,919x = 212,734,035,361
  5. Step 5: Solve for x
    x = 212,734,035,361/289,919
  6. Step 6: Final answer
    x = 733,770.59

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.