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Finding the Third Proportional to 412.69 and 441.75

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Solution

The third proportional to 412.69 and 441.75 is: 472.86

Step by Step Solution

  1. Step 1: Write the proportion equation
    412.69 : 441.75 = 441.75 : x
  2. Step 2: Convert to fraction form
    412.69/441.75 = 441.75/x
  3. Step 3: Cross multiply
    412.69x = 441.75 × 441.75
  4. Step 4: Simplify right side
    412.69x = 195,143.06
  5. Step 5: Solve for x
    x = 195,143.06/412.69
  6. Step 6: Final answer
    x = 472.86

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Why These Related Problems?

These problems maintain the same ratio (1.07) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.