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Finding the Third Proportional to 412.75 and 657.38

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Solution

The third proportional to 412.75 and 657.38 is: 1,046.98

Step by Step Solution

  1. Step 1: Write the proportion equation
    412.75 : 657.38 = 657.38 : x
  2. Step 2: Convert to fraction form
    412.75/657.38 = 657.38/x
  3. Step 3: Cross multiply
    412.75x = 657.38 × 657.38
  4. Step 4: Simplify right side
    412.75x = 432,141.89
  5. Step 5: Solve for x
    x = 432,141.89/412.75
  6. Step 6: Final answer
    x = 1,046.98

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.