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Finding the Third Proportional to 2,209 and 4,471

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Solution

The third proportional to 2,209 and 4,471 is: 9,049.27

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,209 : 4,471 = 4,471 : x
  2. Step 2: Convert to fraction form
    2,209/4,471 = 4,471/x
  3. Step 3: Cross multiply
    2,209x = 4,471 × 4,471
  4. Step 4: Simplify right side
    2,209x = 19,989,841
  5. Step 5: Solve for x
    x = 19,989,841/2,209
  6. Step 6: Final answer
    x = 9,049.27

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Why These Related Problems?

These problems maintain the same ratio (2.02) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.