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Finding the Third Proportional to 31,708 and 67,286

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Solution

The third proportional to 31,708 and 67,286 is: 142,784.34

Step by Step Solution

  1. Step 1: Write the proportion equation
    31,708 : 67,286 = 67,286 : x
  2. Step 2: Convert to fraction form
    31,708/67,286 = 67,286/x
  3. Step 3: Cross multiply
    31,708x = 67,286 × 67,286
  4. Step 4: Simplify right side
    31,708x = 4,527,405,796
  5. Step 5: Solve for x
    x = 4,527,405,796/31,708
  6. Step 6: Final answer
    x = 142,784.34

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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.