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Finding the Third Proportional to 7,729 and 9,771

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Solution

The third proportional to 7,729 and 9,771 is: 12,352.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,729 : 9,771 = 9,771 : x
  2. Step 2: Convert to fraction form
    7,729/9,771 = 9,771/x
  3. Step 3: Cross multiply
    7,729x = 9,771 × 9,771
  4. Step 4: Simplify right side
    7,729x = 95,472,441
  5. Step 5: Solve for x
    x = 95,472,441/7,729
  6. Step 6: Final answer
    x = 12,352.50

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Why These Related Problems?

These problems maintain the same ratio (1.26) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.