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Finding the Third Proportional to 31,827 and 47,730

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Solution

The third proportional to 31,827 and 47,730 is: 71,579.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    31,827 : 47,730 = 47,730 : x
  2. Step 2: Convert to fraction form
    31,827/47,730 = 47,730/x
  3. Step 3: Cross multiply
    31,827x = 47,730 × 47,730
  4. Step 4: Simplify right side
    31,827x = 2,278,152,900
  5. Step 5: Solve for x
    x = 2,278,152,900/31,827
  6. Step 6: Final answer
    x = 71,579.25

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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.