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Finding the Third Proportional to 32,823 and 69,744

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Solution

The third proportional to 32,823 and 69,744 is: 148,195.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    32,823 : 69,744 = 69,744 : x
  2. Step 2: Convert to fraction form
    32,823/69,744 = 69,744/x
  3. Step 3: Cross multiply
    32,823x = 69,744 × 69,744
  4. Step 4: Simplify right side
    32,823x = 4,864,225,536
  5. Step 5: Solve for x
    x = 4,864,225,536/32,823
  6. Step 6: Final answer
    x = 148,195.64

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Why These Related Problems?

These problems maintain the same ratio (2.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.