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Finding the Third Proportional to 4,214 and 9,824

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Solution

The third proportional to 4,214 and 9,824 is: 22,902.46

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,214 : 9,824 = 9,824 : x
  2. Step 2: Convert to fraction form
    4,214/9,824 = 9,824/x
  3. Step 3: Cross multiply
    4,214x = 9,824 × 9,824
  4. Step 4: Simplify right side
    4,214x = 96,510,976
  5. Step 5: Solve for x
    x = 96,510,976/4,214
  6. Step 6: Final answer
    x = 22,902.46

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Why These Related Problems?

These problems maintain the same ratio (2.33) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.