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Finding the Third Proportional to 10,197 and 16,223

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Solution

The third proportional to 10,197 and 16,223 is: 25,810.11

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,197 : 16,223 = 16,223 : x
  2. Step 2: Convert to fraction form
    10,197/16,223 = 16,223/x
  3. Step 3: Cross multiply
    10,197x = 16,223 × 16,223
  4. Step 4: Simplify right side
    10,197x = 263,185,729
  5. Step 5: Solve for x
    x = 263,185,729/10,197
  6. Step 6: Final answer
    x = 25,810.11

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.