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Finding the Third Proportional to 3,078 and 5,742

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Solution

The third proportional to 3,078 and 5,742 is: 10,711.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,078 : 5,742 = 5,742 : x
  2. Step 2: Convert to fraction form
    3,078/5,742 = 5,742/x
  3. Step 3: Cross multiply
    3,078x = 5,742 × 5,742
  4. Step 4: Simplify right side
    3,078x = 32,970,564
  5. Step 5: Solve for x
    x = 32,970,564/3,078
  6. Step 6: Final answer
    x = 10,711.68

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Why These Related Problems?

These problems maintain the same ratio (1.87) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.