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Finding the Third Proportional to 1,038 and 2,051

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Solution

The third proportional to 1,038 and 2,051 is: 4,052.60

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,038 : 2,051 = 2,051 : x
  2. Step 2: Convert to fraction form
    1,038/2,051 = 2,051/x
  3. Step 3: Cross multiply
    1,038x = 2,051 × 2,051
  4. Step 4: Simplify right side
    1,038x = 4,206,601
  5. Step 5: Solve for x
    x = 4,206,601/1,038
  6. Step 6: Final answer
    x = 4,052.60

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Why These Related Problems?

These problems maintain the same ratio (1.98) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.