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Finding the Third Proportional to 463.22 and 522.07

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Solution

The third proportional to 463.22 and 522.07 is: 588.40

Step by Step Solution

  1. Step 1: Write the proportion equation
    463.22 : 522.07 = 522.07 : x
  2. Step 2: Convert to fraction form
    463.22/522.07 = 522.07/x
  3. Step 3: Cross multiply
    463.22x = 522.07 × 522.07
  4. Step 4: Simplify right side
    463.22x = 272,557.41
  5. Step 5: Solve for x
    x = 272,557.41/463.22
  6. Step 6: Final answer
    x = 588.40

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Why These Related Problems?

These problems maintain the same ratio (1.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.