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Finding the Third Proportional to 19,586 and 31,529

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Solution

The third proportional to 19,586 and 31,529 is: 50,754.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    19,586 : 31,529 = 31,529 : x
  2. Step 2: Convert to fraction form
    19,586/31,529 = 31,529/x
  3. Step 3: Cross multiply
    19,586x = 31,529 × 31,529
  4. Step 4: Simplify right side
    19,586x = 994,077,841
  5. Step 5: Solve for x
    x = 994,077,841/19,586
  6. Step 6: Final answer
    x = 50,754.51

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Why These Related Problems?

These problems maintain the same ratio (1.61) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.