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Finding the Third Proportional to 256 and 541.75

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Solution

The third proportional to 256 and 541.75 is: 1,146.46

Step by Step Solution

  1. Step 1: Write the proportion equation
    256 : 541.75 = 541.75 : x
  2. Step 2: Convert to fraction form
    256/541.75 = 541.75/x
  3. Step 3: Cross multiply
    256x = 541.75 × 541.75
  4. Step 4: Simplify right side
    256x = 293,493.06
  5. Step 5: Solve for x
    x = 293,493.06/256
  6. Step 6: Final answer
    x = 1,146.46

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Why These Related Problems?

These problems maintain the same ratio (2.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.