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Finding the Third Proportional to 6,410 and 9,123

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Solution

The third proportional to 6,410 and 9,123 is: 12,984.26

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,410 : 9,123 = 9,123 : x
  2. Step 2: Convert to fraction form
    6,410/9,123 = 9,123/x
  3. Step 3: Cross multiply
    6,410x = 9,123 × 9,123
  4. Step 4: Simplify right side
    6,410x = 83,229,129
  5. Step 5: Solve for x
    x = 83,229,129/6,410
  6. Step 6: Final answer
    x = 12,984.26

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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.