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Finding the Third Proportional to 409 and 657

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Solution

The third proportional to 409 and 657 is: 1,055.38

Step by Step Solution

  1. Step 1: Write the proportion equation
    409 : 657 = 657 : x
  2. Step 2: Convert to fraction form
    409/657 = 657/x
  3. Step 3: Cross multiply
    409x = 657 × 657
  4. Step 4: Simplify right side
    409x = 431,649
  5. Step 5: Solve for x
    x = 431,649/409
  6. Step 6: Final answer
    x = 1,055.38

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Why These Related Problems?

These problems maintain the same ratio (1.61) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.