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Finding the Third Proportional to 2,102 and 2,566

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Solution

The third proportional to 2,102 and 2,566 is: 3,132.42

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,102 : 2,566 = 2,566 : x
  2. Step 2: Convert to fraction form
    2,102/2,566 = 2,566/x
  3. Step 3: Cross multiply
    2,102x = 2,566 × 2,566
  4. Step 4: Simplify right side
    2,102x = 6,584,356
  5. Step 5: Solve for x
    x = 6,584,356/2,102
  6. Step 6: Final answer
    x = 3,132.42

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Why These Related Problems?

These problems maintain the same ratio (1.22) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.