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Finding the Third Proportional to 1,406 and 1,866

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Solution

The third proportional to 1,406 and 1,866 is: 2,476.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,406 : 1,866 = 1,866 : x
  2. Step 2: Convert to fraction form
    1,406/1,866 = 1,866/x
  3. Step 3: Cross multiply
    1,406x = 1,866 × 1,866
  4. Step 4: Simplify right side
    1,406x = 3,481,956
  5. Step 5: Solve for x
    x = 3,481,956/1,406
  6. Step 6: Final answer
    x = 2,476.50

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Why These Related Problems?

These problems maintain the same ratio (1.33) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.