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Finding the Third Proportional to 409 and 768

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Solution

The third proportional to 409 and 768 is: 1,442.11

Step by Step Solution

  1. Step 1: Write the proportion equation
    409 : 768 = 768 : x
  2. Step 2: Convert to fraction form
    409/768 = 768/x
  3. Step 3: Cross multiply
    409x = 768 × 768
  4. Step 4: Simplify right side
    409x = 589,824
  5. Step 5: Solve for x
    x = 589,824/409
  6. Step 6: Final answer
    x = 1,442.11

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Why These Related Problems?

These problems maintain the same ratio (1.88) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.