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Finding the Third Proportional to 419 and 567

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Solution

The third proportional to 419 and 567 is: 767.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    419 : 567 = 567 : x
  2. Step 2: Convert to fraction form
    419/567 = 567/x
  3. Step 3: Cross multiply
    419x = 567 × 567
  4. Step 4: Simplify right side
    419x = 321,489
  5. Step 5: Solve for x
    x = 321,489/419
  6. Step 6: Final answer
    x = 767.28

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Why These Related Problems?

These problems maintain the same ratio (1.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.