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Finding the Third Proportional to 659 and 1,406

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Solution

The third proportional to 659 and 1,406 is: 2,999.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    659 : 1,406 = 1,406 : x
  2. Step 2: Convert to fraction form
    659/1,406 = 1,406/x
  3. Step 3: Cross multiply
    659x = 1,406 × 1,406
  4. Step 4: Simplify right side
    659x = 1,976,836
  5. Step 5: Solve for x
    x = 1,976,836/659
  6. Step 6: Final answer
    x = 2,999.75

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.