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Finding the Third Proportional to 409 and 471

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Solution

The third proportional to 409 and 471 is: 542.40

Step by Step Solution

  1. Step 1: Write the proportion equation
    409 : 471 = 471 : x
  2. Step 2: Convert to fraction form
    409/471 = 471/x
  3. Step 3: Cross multiply
    409x = 471 × 471
  4. Step 4: Simplify right side
    409x = 221,841
  5. Step 5: Solve for x
    x = 221,841/409
  6. Step 6: Final answer
    x = 542.40

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Why These Related Problems?

These problems maintain the same ratio (1.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.