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Finding the Third Proportional to 414 and 869

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Solution

The third proportional to 414 and 869 is: 1,824.06

Step by Step Solution

  1. Step 1: Write the proportion equation
    414 : 869 = 869 : x
  2. Step 2: Convert to fraction form
    414/869 = 869/x
  3. Step 3: Cross multiply
    414x = 869 × 869
  4. Step 4: Simplify right side
    414x = 755,161
  5. Step 5: Solve for x
    x = 755,161/414
  6. Step 6: Final answer
    x = 1,824.06

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Why These Related Problems?

These problems maintain the same ratio (2.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.