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Finding the Third Proportional to 257 and 649

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Solution

The third proportional to 257 and 649 is: 1,638.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    257 : 649 = 649 : x
  2. Step 2: Convert to fraction form
    257/649 = 649/x
  3. Step 3: Cross multiply
    257x = 649 × 649
  4. Step 4: Simplify right side
    257x = 421,201
  5. Step 5: Solve for x
    x = 421,201/257
  6. Step 6: Final answer
    x = 1,638.91

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Why These Related Problems?

These problems maintain the same ratio (2.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.