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Finding the Third Proportional to 414 and 561

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Solution

The third proportional to 414 and 561 is: 760.20

Step by Step Solution

  1. Step 1: Write the proportion equation
    414 : 561 = 561 : x
  2. Step 2: Convert to fraction form
    414/561 = 561/x
  3. Step 3: Cross multiply
    414x = 561 × 561
  4. Step 4: Simplify right side
    414x = 314,721
  5. Step 5: Solve for x
    x = 314,721/414
  6. Step 6: Final answer
    x = 760.20

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Why These Related Problems?

These problems maintain the same ratio (1.36) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.