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Finding the Third Proportional to 289,914 and 461,223

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Solution

The third proportional to 289,914 and 461,223 is: 733,757.79

Step by Step Solution

  1. Step 1: Write the proportion equation
    289,914 : 461,223 = 461,223 : x
  2. Step 2: Convert to fraction form
    289,914/461,223 = 461,223/x
  3. Step 3: Cross multiply
    289,914x = 461,223 × 461,223
  4. Step 4: Simplify right side
    289,914x = 212,726,655,729
  5. Step 5: Solve for x
    x = 212,726,655,729/289,914
  6. Step 6: Final answer
    x = 733,757.79

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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.