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Finding the Third Proportional to 412.31 and 964.88

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Solution

The third proportional to 412.31 and 964.88 is: 2,257.96

Step by Step Solution

  1. Step 1: Write the proportion equation
    412.31 : 964.88 = 964.88 : x
  2. Step 2: Convert to fraction form
    412.31/964.88 = 964.88/x
  3. Step 3: Cross multiply
    412.31x = 964.88 × 964.88
  4. Step 4: Simplify right side
    412.31x = 930,983.77
  5. Step 5: Solve for x
    x = 930,983.77/412.31
  6. Step 6: Final answer
    x = 2,257.96

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Why These Related Problems?

These problems maintain the same ratio (2.34) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.