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Finding the Third Proportional to 31,829 and 47,733

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Solution

The third proportional to 31,829 and 47,733 is: 71,583.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    31,829 : 47,733 = 47,733 : x
  2. Step 2: Convert to fraction form
    31,829/47,733 = 47,733/x
  3. Step 3: Cross multiply
    31,829x = 47,733 × 47,733
  4. Step 4: Simplify right side
    31,829x = 2,278,439,289
  5. Step 5: Solve for x
    x = 2,278,439,289/31,829
  6. Step 6: Final answer
    x = 71,583.75

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.