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Finding the Third Proportional to 19,969 and 27,097

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Solution

The third proportional to 19,969 and 27,097 is: 36,769.36

Step by Step Solution

  1. Step 1: Write the proportion equation
    19,969 : 27,097 = 27,097 : x
  2. Step 2: Convert to fraction form
    19,969/27,097 = 27,097/x
  3. Step 3: Cross multiply
    19,969x = 27,097 × 27,097
  4. Step 4: Simplify right side
    19,969x = 734,247,409
  5. Step 5: Solve for x
    x = 734,247,409/19,969
  6. Step 6: Final answer
    x = 36,769.36

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Why These Related Problems?

These problems maintain the same ratio (1.36) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.