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Finding the Third Proportional to 513 and 727.31

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Solution

The third proportional to 513 and 727.31 is: 1,031.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    513 : 727.31 = 727.31 : x
  2. Step 2: Convert to fraction form
    513/727.31 = 727.31/x
  3. Step 3: Cross multiply
    513x = 727.31 × 727.31
  4. Step 4: Simplify right side
    513x = 528,983.47
  5. Step 5: Solve for x
    x = 528,983.47/513
  6. Step 6: Final answer
    x = 1,031.16

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.