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Finding the Third Proportional to 1,206 and 2,814

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Solution

The third proportional to 1,206 and 2,814 is: 6,566

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,206 : 2,814 = 2,814 : x
  2. Step 2: Convert to fraction form
    1,206/2,814 = 2,814/x
  3. Step 3: Cross multiply
    1,206x = 2,814 × 2,814
  4. Step 4: Simplify right side
    1,206x = 7,918,596
  5. Step 5: Solve for x
    x = 7,918,596/1,206
  6. Step 6: Final answer
    x = 6,566

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Why These Related Problems?

These problems maintain the same ratio (2.33) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.