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Finding the Third Proportional to 256 and 415

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Solution

The third proportional to 256 and 415 is: 672.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    256 : 415 = 415 : x
  2. Step 2: Convert to fraction form
    256/415 = 415/x
  3. Step 3: Cross multiply
    256x = 415 × 415
  4. Step 4: Simplify right side
    256x = 172,225
  5. Step 5: Solve for x
    x = 172,225/256
  6. Step 6: Final answer
    x = 672.75

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Why These Related Problems?

These problems maintain the same ratio (1.62) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.