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Finding the Third Proportional to 1,006 and 1,427

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Solution

The third proportional to 1,006 and 1,427 is: 2,024.18

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,006 : 1,427 = 1,427 : x
  2. Step 2: Convert to fraction form
    1,006/1,427 = 1,427/x
  3. Step 3: Cross multiply
    1,006x = 1,427 × 1,427
  4. Step 4: Simplify right side
    1,006x = 2,036,329
  5. Step 5: Solve for x
    x = 2,036,329/1,006
  6. Step 6: Final answer
    x = 2,024.18

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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.