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Finding the Third Proportional to 27,097 and 65,278

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Solution

The third proportional to 27,097 and 65,278 is: 157,257.90

Step by Step Solution

  1. Step 1: Write the proportion equation
    27,097 : 65,278 = 65,278 : x
  2. Step 2: Convert to fraction form
    27,097/65,278 = 65,278/x
  3. Step 3: Cross multiply
    27,097x = 65,278 × 65,278
  4. Step 4: Simplify right side
    27,097x = 4,261,217,284
  5. Step 5: Solve for x
    x = 4,261,217,284/27,097
  6. Step 6: Final answer
    x = 157,257.90

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Why These Related Problems?

These problems maintain the same ratio (2.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.