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Finding the Third Proportional to 1,412 and 2,006

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Solution

The third proportional to 1,412 and 2,006 is: 2,849.88

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,412 : 2,006 = 2,006 : x
  2. Step 2: Convert to fraction form
    1,412/2,006 = 2,006/x
  3. Step 3: Cross multiply
    1,412x = 2,006 × 2,006
  4. Step 4: Simplify right side
    1,412x = 4,024,036
  5. Step 5: Solve for x
    x = 4,024,036/1,412
  6. Step 6: Final answer
    x = 2,849.88

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.