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Finding the Third Proportional to 419 and 680

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Solution

The third proportional to 419 and 680 is: 1,103.58

Step by Step Solution

  1. Step 1: Write the proportion equation
    419 : 680 = 680 : x
  2. Step 2: Convert to fraction form
    419/680 = 680/x
  3. Step 3: Cross multiply
    419x = 680 × 680
  4. Step 4: Simplify right side
    419x = 462,400
  5. Step 5: Solve for x
    x = 462,400/419
  6. Step 6: Final answer
    x = 1,103.58

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Why These Related Problems?

These problems maintain the same ratio (1.62) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.