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Finding the Third Proportional to 19,705 and 31,198

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Solution

The third proportional to 19,705 and 31,198 is: 49,394.33

Step by Step Solution

  1. Step 1: Write the proportion equation
    19,705 : 31,198 = 31,198 : x
  2. Step 2: Convert to fraction form
    19,705/31,198 = 31,198/x
  3. Step 3: Cross multiply
    19,705x = 31,198 × 31,198
  4. Step 4: Simplify right side
    19,705x = 973,315,204
  5. Step 5: Solve for x
    x = 973,315,204/19,705
  6. Step 6: Final answer
    x = 49,394.33

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Why These Related Problems?

These problems maintain the same ratio (1.58) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.