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Finding the Third Proportional to 691 and 1,591

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Solution

The third proportional to 691 and 1,591 is: 3,663.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    691 : 1,591 = 1,591 : x
  2. Step 2: Convert to fraction form
    691/1,591 = 1,591/x
  3. Step 3: Cross multiply
    691x = 1,591 × 1,591
  4. Step 4: Simplify right side
    691x = 2,531,281
  5. Step 5: Solve for x
    x = 2,531,281/691
  6. Step 6: Final answer
    x = 3,663.21

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Why These Related Problems?

These problems maintain the same ratio (2.30) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.