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Finding the Third Proportional to 120 and 256

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Solution

The third proportional to 120 and 256 is: 546.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    120 : 256 = 256 : x
  2. Step 2: Convert to fraction form
    120/256 = 256/x
  3. Step 3: Cross multiply
    120x = 256 × 256
  4. Step 4: Simplify right side
    120x = 65,536
  5. Step 5: Solve for x
    x = 65,536/120
  6. Step 6: Final answer
    x = 546.13

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.