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Finding the Third Proportional to 2,709 and 5,623

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Solution

The third proportional to 2,709 and 5,623 is: 11,671.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,709 : 5,623 = 5,623 : x
  2. Step 2: Convert to fraction form
    2,709/5,623 = 5,623/x
  3. Step 3: Cross multiply
    2,709x = 5,623 × 5,623
  4. Step 4: Simplify right side
    2,709x = 31,618,129
  5. Step 5: Solve for x
    x = 31,618,129/2,709
  6. Step 6: Final answer
    x = 11,671.51

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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.