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Finding the Third Proportional to 649 and 1,424

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Solution

The third proportional to 649 and 1,424 is: 3,124.46

Step by Step Solution

  1. Step 1: Write the proportion equation
    649 : 1,424 = 1,424 : x
  2. Step 2: Convert to fraction form
    649/1,424 = 1,424/x
  3. Step 3: Cross multiply
    649x = 1,424 × 1,424
  4. Step 4: Simplify right side
    649x = 2,027,776
  5. Step 5: Solve for x
    x = 2,027,776/649
  6. Step 6: Final answer
    x = 3,124.46

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.