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Finding the Third Proportional to 417.75 and 649.38

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Solution

The third proportional to 417.75 and 649.38 is: 1,009.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    417.75 : 649.38 = 649.38 : x
  2. Step 2: Convert to fraction form
    417.75/649.38 = 649.38/x
  3. Step 3: Cross multiply
    417.75x = 649.38 × 649.38
  4. Step 4: Simplify right side
    417.75x = 421,687.89
  5. Step 5: Solve for x
    x = 421,687.89/417.75
  6. Step 6: Final answer
    x = 1,009.43

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.