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Finding the Third Proportional to 285,905 and 419,308

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Solution

The third proportional to 285,905 and 419,308 is: 614,956.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    285,905 : 419,308 = 419,308 : x
  2. Step 2: Convert to fraction form
    285,905/419,308 = 419,308/x
  3. Step 3: Cross multiply
    285,905x = 419,308 × 419,308
  4. Step 4: Simplify right side
    285,905x = 175,819,198,864
  5. Step 5: Solve for x
    x = 175,819,198,864/285,905
  6. Step 6: Final answer
    x = 614,956.71

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.