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Finding the Third Proportional to 277,418 and 419,043

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Solution

The third proportional to 277,418 and 419,043 is: 632,969.15

Step by Step Solution

  1. Step 1: Write the proportion equation
    277,418 : 419,043 = 419,043 : x
  2. Step 2: Convert to fraction form
    277,418/419,043 = 419,043/x
  3. Step 3: Cross multiply
    277,418x = 419,043 × 419,043
  4. Step 4: Simplify right side
    277,418x = 175,597,035,849
  5. Step 5: Solve for x
    x = 175,597,035,849/277,418
  6. Step 6: Final answer
    x = 632,969.15

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.