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Finding the Third Proportional to 2,729 and 6,097

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Solution

The third proportional to 2,729 and 6,097 is: 13,621.62

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,729 : 6,097 = 6,097 : x
  2. Step 2: Convert to fraction form
    2,729/6,097 = 6,097/x
  3. Step 3: Cross multiply
    2,729x = 6,097 × 6,097
  4. Step 4: Simplify right side
    2,729x = 37,173,409
  5. Step 5: Solve for x
    x = 37,173,409/2,729
  6. Step 6: Final answer
    x = 13,621.62

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Why These Related Problems?

These problems maintain the same ratio (2.23) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.