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Finding the Third Proportional to 406.69 and 461.81

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Solution

The third proportional to 406.69 and 461.81 is: 524.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    406.69 : 461.81 = 461.81 : x
  2. Step 2: Convert to fraction form
    406.69/461.81 = 461.81/x
  3. Step 3: Cross multiply
    406.69x = 461.81 × 461.81
  4. Step 4: Simplify right side
    406.69x = 213,270.79
  5. Step 5: Solve for x
    x = 213,270.79/406.69
  6. Step 6: Final answer
    x = 524.41

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Why These Related Problems?

These problems maintain the same ratio (1.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.