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Finding the Third Proportional to 4,024 and 5,742

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Solution

The third proportional to 4,024 and 5,742 is: 8,193.48

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,024 : 5,742 = 5,742 : x
  2. Step 2: Convert to fraction form
    4,024/5,742 = 5,742/x
  3. Step 3: Cross multiply
    4,024x = 5,742 × 5,742
  4. Step 4: Simplify right side
    4,024x = 32,970,564
  5. Step 5: Solve for x
    x = 32,970,564/4,024
  6. Step 6: Final answer
    x = 8,193.48

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Why These Related Problems?

These problems maintain the same ratio (1.43) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.