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Finding the Third Proportional to 4,024 and 5,824

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Solution

The third proportional to 4,024 and 5,824 is: 8,429.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,024 : 5,824 = 5,824 : x
  2. Step 2: Convert to fraction form
    4,024/5,824 = 5,824/x
  3. Step 3: Cross multiply
    4,024x = 5,824 × 5,824
  4. Step 4: Simplify right side
    4,024x = 33,918,976
  5. Step 5: Solve for x
    x = 33,918,976/4,024
  6. Step 6: Final answer
    x = 8,429.17

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Why These Related Problems?

These problems maintain the same ratio (1.45) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.