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Finding the Third Proportional to 19,782 and 31,302

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Solution

The third proportional to 19,782 and 31,302 is: 49,530.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    19,782 : 31,302 = 31,302 : x
  2. Step 2: Convert to fraction form
    19,782/31,302 = 31,302/x
  3. Step 3: Cross multiply
    19,782x = 31,302 × 31,302
  4. Step 4: Simplify right side
    19,782x = 979,815,204
  5. Step 5: Solve for x
    x = 979,815,204/19,782
  6. Step 6: Final answer
    x = 49,530.64

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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.