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Finding the Third Proportional to 3,840 and 6,123

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Solution

The third proportional to 3,840 and 6,123 is: 9,763.31

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,840 : 6,123 = 6,123 : x
  2. Step 2: Convert to fraction form
    3,840/6,123 = 6,123/x
  3. Step 3: Cross multiply
    3,840x = 6,123 × 6,123
  4. Step 4: Simplify right side
    3,840x = 37,491,129
  5. Step 5: Solve for x
    x = 37,491,129/3,840
  6. Step 6: Final answer
    x = 9,763.31

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.