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Finding the Third Proportional to 256 and 280

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Solution

The third proportional to 256 and 280 is: 306.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    256 : 280 = 280 : x
  2. Step 2: Convert to fraction form
    256/280 = 280/x
  3. Step 3: Cross multiply
    256x = 280 × 280
  4. Step 4: Simplify right side
    256x = 78,400
  5. Step 5: Solve for x
    x = 78,400/256
  6. Step 6: Final answer
    x = 306.25

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.