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Finding the Third Proportional to 2,209 and 4,601

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Solution

The third proportional to 2,209 and 4,601 is: 9,583.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,209 : 4,601 = 4,601 : x
  2. Step 2: Convert to fraction form
    2,209/4,601 = 4,601/x
  3. Step 3: Cross multiply
    2,209x = 4,601 × 4,601
  4. Step 4: Simplify right side
    2,209x = 21,169,201
  5. Step 5: Solve for x
    x = 21,169,201/2,209
  6. Step 6: Final answer
    x = 9,583.16

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Why These Related Problems?

These problems maintain the same ratio (2.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.