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Finding the Third Proportional to 6,309 and 13,729

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Solution

The third proportional to 6,309 and 13,729 is: 29,875.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,309 : 13,729 = 13,729 : x
  2. Step 2: Convert to fraction form
    6,309/13,729 = 13,729/x
  3. Step 3: Cross multiply
    6,309x = 13,729 × 13,729
  4. Step 4: Simplify right side
    6,309x = 188,485,441
  5. Step 5: Solve for x
    x = 188,485,441/6,309
  6. Step 6: Final answer
    x = 29,875.64

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.