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Finding the Third Proportional to 5,410 and 8,123

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Solution

The third proportional to 5,410 and 8,123 is: 12,196.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,410 : 8,123 = 8,123 : x
  2. Step 2: Convert to fraction form
    5,410/8,123 = 8,123/x
  3. Step 3: Cross multiply
    5,410x = 8,123 × 8,123
  4. Step 4: Simplify right side
    5,410x = 65,983,129
  5. Step 5: Solve for x
    x = 65,983,129/5,410
  6. Step 6: Final answer
    x = 12,196.51

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.