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Finding the Third Proportional to 407 and 542

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Solution

The third proportional to 407 and 542 is: 721.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    407 : 542 = 542 : x
  2. Step 2: Convert to fraction form
    407/542 = 542/x
  3. Step 3: Cross multiply
    407x = 542 × 542
  4. Step 4: Simplify right side
    407x = 293,764
  5. Step 5: Solve for x
    x = 293,764/407
  6. Step 6: Final answer
    x = 721.78

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Why These Related Problems?

These problems maintain the same ratio (1.33) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.