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Finding the Third Proportional to 2,102 and 2,982

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Solution

The third proportional to 2,102 and 2,982 is: 4,230.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,102 : 2,982 = 2,982 : x
  2. Step 2: Convert to fraction form
    2,102/2,982 = 2,982/x
  3. Step 3: Cross multiply
    2,102x = 2,982 × 2,982
  4. Step 4: Simplify right side
    2,102x = 8,892,324
  5. Step 5: Solve for x
    x = 8,892,324/2,102
  6. Step 6: Final answer
    x = 4,230.41

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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.