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Finding the Third Proportional to 14,586 and 20,097

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Solution

The third proportional to 14,586 and 20,097 is: 27,690.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    14,586 : 20,097 = 20,097 : x
  2. Step 2: Convert to fraction form
    14,586/20,097 = 20,097/x
  3. Step 3: Cross multiply
    14,586x = 20,097 × 20,097
  4. Step 4: Simplify right side
    14,586x = 403,889,409
  5. Step 5: Solve for x
    x = 403,889,409/14,586
  6. Step 6: Final answer
    x = 27,690.21

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.