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Finding the Third Proportional to 462.14 and 649.97

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Solution

The third proportional to 462.14 and 649.97 is: 914.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    462.14 : 649.97 = 649.97 : x
  2. Step 2: Convert to fraction form
    462.14/649.97 = 649.97/x
  3. Step 3: Cross multiply
    462.14x = 649.97 × 649.97
  4. Step 4: Simplify right side
    462.14x = 422,459.38
  5. Step 5: Solve for x
    x = 422,459.38/462.14
  6. Step 6: Final answer
    x = 914.14

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.