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Finding the Third Proportional to 462 and 512.25

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Solution

The third proportional to 462 and 512.25 is: 567.97

Step by Step Solution

  1. Step 1: Write the proportion equation
    462 : 512.25 = 512.25 : x
  2. Step 2: Convert to fraction form
    462/512.25 = 512.25/x
  3. Step 3: Cross multiply
    462x = 512.25 × 512.25
  4. Step 4: Simplify right side
    462x = 262,400.06
  5. Step 5: Solve for x
    x = 262,400.06/462
  6. Step 6: Final answer
    x = 567.97

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Why These Related Problems?

These problems maintain the same ratio (1.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.