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Finding the Third Proportional to 32,306 and 69,704

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Solution

The third proportional to 32,306 and 69,704 is: 150,394.59

Step by Step Solution

  1. Step 1: Write the proportion equation
    32,306 : 69,704 = 69,704 : x
  2. Step 2: Convert to fraction form
    32,306/69,704 = 69,704/x
  3. Step 3: Cross multiply
    32,306x = 69,704 × 69,704
  4. Step 4: Simplify right side
    32,306x = 4,858,647,616
  5. Step 5: Solve for x
    x = 4,858,647,616/32,306
  6. Step 6: Final answer
    x = 150,394.59

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.