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Finding the Third Proportional to 691 and 811

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Solution

The third proportional to 691 and 811 is: 951.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    691 : 811 = 811 : x
  2. Step 2: Convert to fraction form
    691/811 = 811/x
  3. Step 3: Cross multiply
    691x = 811 × 811
  4. Step 4: Simplify right side
    691x = 657,721
  5. Step 5: Solve for x
    x = 657,721/691
  6. Step 6: Final answer
    x = 951.84

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Why These Related Problems?

These problems maintain the same ratio (1.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.