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Finding the Third Proportional to 419,492 and 593,013

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Solution

The third proportional to 419,492 and 593,013 is: 838,310.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    419,492 : 593,013 = 593,013 : x
  2. Step 2: Convert to fraction form
    419,492/593,013 = 593,013/x
  3. Step 3: Cross multiply
    419,492x = 593,013 × 593,013
  4. Step 4: Simplify right side
    419,492x = 351,664,418,169
  5. Step 5: Solve for x
    x = 351,664,418,169/419,492
  6. Step 6: Final answer
    x = 838,310.19

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.