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Finding the Third Proportional to 419 and 853

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Solution

The third proportional to 419 and 853 is: 1,736.54

Step by Step Solution

  1. Step 1: Write the proportion equation
    419 : 853 = 853 : x
  2. Step 2: Convert to fraction form
    419/853 = 853/x
  3. Step 3: Cross multiply
    419x = 853 × 853
  4. Step 4: Simplify right side
    419x = 727,609
  5. Step 5: Solve for x
    x = 727,609/419
  6. Step 6: Final answer
    x = 1,736.54

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Why These Related Problems?

These problems maintain the same ratio (2.04) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.