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Finding the Third Proportional to 8,197 and 17,623

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Solution

The third proportional to 8,197 and 17,623 is: 37,888.27

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,197 : 17,623 = 17,623 : x
  2. Step 2: Convert to fraction form
    8,197/17,623 = 17,623/x
  3. Step 3: Cross multiply
    8,197x = 17,623 × 17,623
  4. Step 4: Simplify right side
    8,197x = 310,570,129
  5. Step 5: Solve for x
    x = 310,570,129/8,197
  6. Step 6: Final answer
    x = 37,888.27

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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.