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Finding the Third Proportional to 691 and 1,699

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Solution

The third proportional to 691 and 1,699 is: 4,177.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    691 : 1,699 = 1,699 : x
  2. Step 2: Convert to fraction form
    691/1,699 = 1,699/x
  3. Step 3: Cross multiply
    691x = 1,699 × 1,699
  4. Step 4: Simplify right side
    691x = 2,886,601
  5. Step 5: Solve for x
    x = 2,886,601/691
  6. Step 6: Final answer
    x = 4,177.43

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Why These Related Problems?

These problems maintain the same ratio (2.46) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.