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Finding the Third Proportional to 1,206 and 1,809

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Solution

The third proportional to 1,206 and 1,809 is: 2,713.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,206 : 1,809 = 1,809 : x
  2. Step 2: Convert to fraction form
    1,206/1,809 = 1,809/x
  3. Step 3: Cross multiply
    1,206x = 1,809 × 1,809
  4. Step 4: Simplify right side
    1,206x = 3,272,481
  5. Step 5: Solve for x
    x = 3,272,481/1,206
  6. Step 6: Final answer
    x = 2,713.50

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.