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Finding the Third Proportional to 523 and 814

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Solution

The third proportional to 523 and 814 is: 1,266.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    523 : 814 = 814 : x
  2. Step 2: Convert to fraction form
    523/814 = 814/x
  3. Step 3: Cross multiply
    523x = 814 × 814
  4. Step 4: Simplify right side
    523x = 662,596
  5. Step 5: Solve for x
    x = 662,596/523
  6. Step 6: Final answer
    x = 1,266.91

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Why These Related Problems?

These problems maintain the same ratio (1.56) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.