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Finding the Third Proportional to 684 and 1,649

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Solution

The third proportional to 684 and 1,649 is: 3,975.44

Step by Step Solution

  1. Step 1: Write the proportion equation
    684 : 1,649 = 1,649 : x
  2. Step 2: Convert to fraction form
    684/1,649 = 1,649/x
  3. Step 3: Cross multiply
    684x = 1,649 × 1,649
  4. Step 4: Simplify right side
    684x = 2,719,201
  5. Step 5: Solve for x
    x = 2,719,201/684
  6. Step 6: Final answer
    x = 3,975.44

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Why These Related Problems?

These problems maintain the same ratio (2.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.