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Finding the Third Proportional to 463 and 1,006

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Solution

The third proportional to 463 and 1,006 is: 2,185.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    463 : 1,006 = 1,006 : x
  2. Step 2: Convert to fraction form
    463/1,006 = 1,006/x
  3. Step 3: Cross multiply
    463x = 1,006 × 1,006
  4. Step 4: Simplify right side
    463x = 1,012,036
  5. Step 5: Solve for x
    x = 1,012,036/463
  6. Step 6: Final answer
    x = 2,185.82

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.