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Finding the Third Proportional to 409 and 678

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Solution

The third proportional to 409 and 678 is: 1,123.92

Step by Step Solution

  1. Step 1: Write the proportion equation
    409 : 678 = 678 : x
  2. Step 2: Convert to fraction form
    409/678 = 678/x
  3. Step 3: Cross multiply
    409x = 678 × 678
  4. Step 4: Simplify right side
    409x = 459,684
  5. Step 5: Solve for x
    x = 459,684/409
  6. Step 6: Final answer
    x = 1,123.92

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Why These Related Problems?

These problems maintain the same ratio (1.66) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.