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Finding the Third Proportional to 31,684 and 47,431

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Solution

The third proportional to 31,684 and 47,431 is: 71,004.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    31,684 : 47,431 = 47,431 : x
  2. Step 2: Convert to fraction form
    31,684/47,431 = 47,431/x
  3. Step 3: Cross multiply
    31,684x = 47,431 × 47,431
  4. Step 4: Simplify right side
    31,684x = 2,249,699,761
  5. Step 5: Solve for x
    x = 2,249,699,761/31,684
  6. Step 6: Final answer
    x = 71,004.28

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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.