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Finding the Third Proportional to 8,224 and 17,678

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Solution

The third proportional to 8,224 and 17,678 is: 37,999.96

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,224 : 17,678 = 17,678 : x
  2. Step 2: Convert to fraction form
    8,224/17,678 = 17,678/x
  3. Step 3: Cross multiply
    8,224x = 17,678 × 17,678
  4. Step 4: Simplify right side
    8,224x = 312,511,684
  5. Step 5: Solve for x
    x = 312,511,684/8,224
  6. Step 6: Final answer
    x = 37,999.96

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.