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Finding the Third Proportional to 5,209 and 7,866

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Solution

The third proportional to 5,209 and 7,866 is: 11,878.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,209 : 7,866 = 7,866 : x
  2. Step 2: Convert to fraction form
    5,209/7,866 = 7,866/x
  3. Step 3: Cross multiply
    5,209x = 7,866 × 7,866
  4. Step 4: Simplify right side
    5,209x = 61,873,956
  5. Step 5: Solve for x
    x = 61,873,956/5,209
  6. Step 6: Final answer
    x = 11,878.28

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.