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Finding the Third Proportional to 523 and 816

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Solution

The third proportional to 523 and 816 is: 1,273.15

Step by Step Solution

  1. Step 1: Write the proportion equation
    523 : 816 = 816 : x
  2. Step 2: Convert to fraction form
    523/816 = 816/x
  3. Step 3: Cross multiply
    523x = 816 × 816
  4. Step 4: Simplify right side
    523x = 665,856
  5. Step 5: Solve for x
    x = 665,856/523
  6. Step 6: Final answer
    x = 1,273.15

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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.