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Finding the Third Proportional to 32,770 and 69,823

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Solution

The third proportional to 32,770 and 69,823 is: 148,771.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    32,770 : 69,823 = 69,823 : x
  2. Step 2: Convert to fraction form
    32,770/69,823 = 69,823/x
  3. Step 3: Cross multiply
    32,770x = 69,823 × 69,823
  4. Step 4: Simplify right side
    32,770x = 4,875,251,329
  5. Step 5: Solve for x
    x = 4,875,251,329/32,770
  6. Step 6: Final answer
    x = 148,771.78

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.