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Finding the Third Proportional to 2,147 and 2,597

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Solution

The third proportional to 2,147 and 2,597 is: 3,141.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,147 : 2,597 = 2,597 : x
  2. Step 2: Convert to fraction form
    2,147/2,597 = 2,597/x
  3. Step 3: Cross multiply
    2,147x = 2,597 × 2,597
  4. Step 4: Simplify right side
    2,147x = 6,744,409
  5. Step 5: Solve for x
    x = 6,744,409/2,147
  6. Step 6: Final answer
    x = 3,141.32

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Why These Related Problems?

These problems maintain the same ratio (1.21) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.