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Finding the Third Proportional to 296,084 and 419,124

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Solution

The third proportional to 296,084 and 419,124 is: 593,294.23

Step by Step Solution

  1. Step 1: Write the proportion equation
    296,084 : 419,124 = 419,124 : x
  2. Step 2: Convert to fraction form
    296,084/419,124 = 419,124/x
  3. Step 3: Cross multiply
    296,084x = 419,124 × 419,124
  4. Step 4: Simplify right side
    296,084x = 175,664,927,376
  5. Step 5: Solve for x
    x = 175,664,927,376/296,084
  6. Step 6: Final answer
    x = 593,294.23

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.