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Finding the Third Proportional to 2,369 and 5,209

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Solution

The third proportional to 2,369 and 5,209 is: 11,453.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,369 : 5,209 = 5,209 : x
  2. Step 2: Convert to fraction form
    2,369/5,209 = 5,209/x
  3. Step 3: Cross multiply
    2,369x = 5,209 × 5,209
  4. Step 4: Simplify right side
    2,369x = 27,133,681
  5. Step 5: Solve for x
    x = 27,133,681/2,369
  6. Step 6: Final answer
    x = 11,453.64

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Why These Related Problems?

These problems maintain the same ratio (2.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.